2021-12-01.  rea.rtr

263 propositions are proved in the file:

        ~/git/minlog/lib/rea.scm

Ignoring intial 0 lemmata, the reference trees for the remaining
263 lemmata are as follows

EqPTotalNatToRatLeft
|- allnc as^1,as^2(
     allnc n^1,n^2(EqPNat n^1 n^2 -> EqPRat(as^1 n^1)(as^2 n^2)) -> 
     allnc n^(TotalNat n^ -> TotalRat(as^1 n^)))

EqPTotalNatToRatRight
|- allnc as^1,as^2(
     allnc n^1,n^2(EqPNat n^1 n^2 -> EqPRat(as^1 n^1)(as^2 n^2)) -> 
     allnc n^(TotalNat n^ -> TotalRat(as^2 n^)))

EqPTotalPosToNatLeft
|- allnc M^1,M^2(
     allnc p^,p^0(EqPPos p^ p^0 -> EqPNat(M^1 p^)(M^2 p^0)) -> 
     allnc p^(TotalPos p^ -> TotalNat(M^1 p^)))

EqPTotalPosToNatRight
|- allnc M^1,M^2(
     allnc p^,p^0(EqPPos p^ p^0 -> EqPNat(M^1 p^)(M^2 p^0)) -> 
     allnc p^(TotalPos p^ -> TotalNat(M^2 p^)))

EqPReaToTotalLeft [2, 1]
|- allnc x^,y^(EqPRea x^ y^ -> TotalRea x^)
   | EqPTotalNatToRatLeft
   | EqPTotalPosToNatLeft

EqPReaToTotalRight [2, 1]
|- allnc x^,y^(EqPRea x^ y^ -> TotalRea y^)
   | EqPTotalNatToRatRight
   | EqPTotalPosToNatRight

EqPReaRefl
|- allnc x^(TotalRea x^ -> EqPRea x^ x^)

ReaTotalVar
|- all x TotalRea x

EqPReaAux
|- allnc as^,M^,bs^,N^(
 EqPRea(RealConstr as^ M^)(RealConstr bs^ N^) ->
 (Pvar rea rea)(RealConstr as^ M^)(RealConstr bs^ N^)) -> 
 allnc x^,y^(EqPRea x^ y^ -> (Pvar rea rea)x^ y^)

EqPReaElimLeft
|- allnc x^,y^(EqP x^ y^ -> EqP(x^ seq)(y^ seq))

EqPReaElimRight
|- allnc x^,y^(EqP x^ y^ -> EqP(x^ mod)(y^ mod))

EqPReaElimLeftRealConstr
|- allnc as^,M^,bs^,N^(
 EqPRea(RealConstr as^ M^)(RealConstr bs^ N^) ->
 allnc n^,m^(EqPNat n^ m^ -> EqPRat(as^ n^)(bs^ m^)))

EqPReaElimRightRealConstr
|- allnc as^,M^,bs^,N^(
 EqPRea(RealConstr as^ M^)(RealConstr bs^ N^) ->
 allnc p^,q^(EqPPos p^ q^ -> EqPNat(M^ p^)(N^ q^)))

CauchyElim
|- 

MonElim
|- allnc M(Mon M -> allnc p,q(p<=q -> M p<=M q))

EfCauchy
|- F -> allnc as,M Cauchy as M

EfMon
|- F -> allnc M Mon M

CauchyChar1 [1, 1]
|- all as,M(Cauchy as M ->
 all p,n,m(M p<=n -> M p<=m -> as n<=as m+(12**p)))
   | CauchyElim

CauchyChar2
|- all as,M(all p,n,m(M p<=n -> M p<=m -> as n<=as m+(12**p)) ->
 Cauchy as M)

RealToCauchy
|- all x(Real x -> Cauchy(x seq)(x mod))

RealToMon
|- all x(Real x -> Mon(x mod))

RealConstrToCauchy
|- all as,M(Real(RealConstr as M) -> Cauchy as M)

RealConstrToMon
|- all as,M(Real(RealConstr as M) -> Mon M)

EfReal [2, 1]
|- F -> all x Real x
   | EfCauchy
   | EfMon

RealRat
|- allnc a Real a

ListNatMaxEqP
|- allnc ns^1,ns^2(EqP ns^1 ns^2 ->
 EqP(ListNatMax ns^1)(ListNatMax ns^2))

ListNatMaxUB
|- all ms,n(n<Lh ms -> ListNatProj n ms<=ListNatMax ms)

ListNatMaxFBar [1, 1]
|- all nat=>nat,n,l(n<l -> (nat=>nat)n<=ListNatMax((nat=>nat)fbar l))
   | ListNatMaxUB

cRatLeBoundTotal
|- 

RBd
|- all as,M(Cauchy as M -> exl n n=RealBd as M)

RBdExFree
|- all as,M(Cauchy as M -> cRBd as M=RealBd as M)

RealBdProp [1, 1]
|- all as,M(Cauchy as M -> all n abs(as n)<=2**cRBd as M)
   | CauchyElim

RealBdPos
|- all as,M Zero<cRBd as M

RealLeAntiSym
|- all x,y(x<<=y -> y<<=x -> RealEq x y)

RealLeElim0
|- all x,y(x<<=y -> Real x)

RealLeElim1
|- all x,y(x<<=y -> Real y)

RealLeElim2
|- all x,y(x<<=y ->
  all p x seq(x mod(PosS p))<=y seq(y mod(PosS p))+(12**p))

RealConstrLeElim2
|- 

RealEqElim0
|- all x,y(x===y -> x<<=y)

RealEqElim1
|- all x,y(x===y -> y<<=x)

RealEqToReal0 [2, 1]
|- all x,y(x===y -> Real x)
   | RealLeElim0
   | RealEqElim0

RealEqToReal1 [2, 1]
|- all x,y(x===y -> Real y)
   | RealLeElim1
   | RealEqElim0

RealEqSElim
|- all x,y(x=+=y -> all n x seq n==y seq n)

RealConstrEqSElim
|- 

TotalReaToEqD
|- allnc x^(TotalReaNc x^ -> x^ eqd RealConstr x^ seq x^ mod)

RealNNegElim0
|- all x(RealNNeg x -> Real x)

RealNNegElim1
|- all x(RealNNeg x -> all p 0<=x seq(x mod p)+(12**p))

RealConstrNNegElim0
|- 

RealConstrNNegElim1
|- 

EfRealLe [2, 2]
|- F -> all x,y x<<=y
   | EfReal [2, 1]
      | EfCauchy
      | EfMon
   | EfReal [2, 1]
      | EfCauchy
      | EfMon

RealLeRefl
|- all x(Real x -> x<<=x)

EfRealEq [2, 3]
|- F -> all x,y x===y
   | EfRealLe [2, 2]
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
   | EfRealLe [2, 2]
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
      | EfReal [2, 1]
         | EfCauchy
         | EfMon

EfRealEqS
|- F -> all x,y x=+=y

EfRealNNeg [1, 2]
|- F -> all x RealNNeg x
   | EfReal [2, 1]
      | EfCauchy
      | EfMon

RealLeChar1 [5, 1]
|- allnc as,M,bs,N(RealConstr as M<<=RealConstr bs N -> 
      allnc p exnc n1 allnc n(n1<=n -> as n<=bs n+(12**p)))
   | CauchyElim
   | RealConstrToCauchy
   | RealConstrLeElim2
   | CauchyElim
   | RealConstrToCauchy

RealLeChar1RealConstrFree [1, 2]
|- all x,y(x<<=y ->
 all p exnc n0 all n(n0<=n -> x seq n<=y seq n+(12**p)))
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy

RealLeChar2 [4, 1]
|- all as,M,bs,N(Real(RealConstr as M) -> Real(RealConstr bs N) ->
           all p exnc n0 all n(n0<=n -> as n<=bs n+(12**p)) ->
           RealConstr as M<<=RealConstr bs N)
   | CauchyElim
   | RealConstrToCauchy
   | CauchyElim
   | RealConstrToCauchy

RealLeChar2RealConstrFree [1, 2]
|- all x,y(Real x -> Real y -> 
 all p exnc n0 all n(n0<=n -> x seq n<=y seq n+(12**p)) -> x<<=y)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy

RealEqChar1
|- all x,y(x===y ->
  all p exnc n1 all n(n1<=n -> abs(x seq n+ ~(y seq n))<=(12**p)))

RealEqChar2 [2, 3]
|- all x,y(Real x -> Real y -> 
 all p exnc n0 all n(n0<=n -> abs(x seq n+ ~(y seq n))<=(12**p)) -> x===y)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealLeTrans [3, 2]
|- all x,y,z(x<<=y -> y<<=z -> x<<=z)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy

RealEqRefl [2, 1]
|- all x(Real x -> x===x)
   | RealLeRefl
   | RealLeRefl

RealEqSym
|- all x,y(x===y -> y===x)

RealEqTrans [6, 3]
|- all x,y,z(x===y -> y===z -> x===z)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealEqElim0
   | RealEqElim0
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealEqElim1
   | RealEqElim1

RealSeqLeToLe [1, 2]
|- all x,y,n1(Real x -> Real y ->
 all n(n1<=n -> x seq n<=y seq n) -> x<<=y)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy

RealSeqEqToEq [2, 3]
|- all x,y,n1(Real x -> Real y ->
 all n(n1<=n -> x seq n==y seq n) -> x===y)
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RatLeToRealLe
|- all a,b(a<=b -> a<<=b)

RealLeToRatLe
|- all a,b(a<<=b -> a<=b)

IntLeToRealLe [1, 1]
|- all k,j(k<=j -> k<<=j)
   | RatLeToRealLe

RealLeToIntLe
|- all k,j(k<<=j -> k<=j)

RealEqSToEq [2, 4]
|- all x,y(Real x -> Real y -> x=+=y -> x===y)
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealEqSElim

CauchyModIncr [1, 1]
|- all M,N,as(all p M p<=N p -> Cauchy as M -> Cauchy as N)
   | CauchyElim

RealModIncr [2, 4]
|- all as,M,N(Real(RealConstr as M) ->
 all p M p<=N p -> Mon N -> RealConstr as M===RealConstr as N)
   | CauchyModIncr [1, 1]
      | CauchyElim
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealLeSElim
|- all x,y(x<+=y -> all n x seq n<=y seq n)

RealConstrLeSElim
|- 

RealLeSToLe [2, 2]
|- all x,y(Real x -> Real y -> x<+=y -> x<<=y)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealConstrLeSElim

RealNNegChar1 [4, 1]
|- all as,M(RealNNeg(RealConstr as M) -> 
      all p exnc n1 all n(n1<=n -> ~(12**p)<=as n))
   | RealConstrNNegElim1
   | CauchyElim
   | RealConstrToCauchy
   | RealNNegElim0

RealNNegChar1RealConstrFree
|- 

RealNNegChar2 [2, 1]
|- all as,M(Real(RealConstr as M) ->
      all p exnc n1 all n(n1<=n -> ~(12**p)<=as n) ->
      RealNNeg(RealConstr as M))
   | CauchyElim
   | RealConstrToCauchy

RealNNegChar2RealConstrFree
|- 

RealNNegSElim
|- all x(RealNNegS x -> all n 0<=x seq n)

RealNNegSToNNeg
|- all x(Real x -> RealNNegS x -> RealNNeg x)

RealNNegToZeroLe [1, 3]
|- all x(RealNNeg x -> 0<<=x)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealZeroLeToNNeg [1, 1]
|- all x(0<<=x -> RealNNeg x)
   | RealNNegChar2RealConstrFree

RealPosChar1 [2, 1]
|- all as,M,p(
 Real(RealConstr as M) -> RealPos(RealConstr as M)p ->
 all n(M(PosS p)<=n -> (12**PosS p)<=as n))
   | CauchyElim
   | RealConstrToCauchy

RealPosChar1RealConstrFree [1, 2]
|- all x,p(Real x -> RealPos x p ->
                   all n(x mod(PosS p)<=n -> (12**PosS p)<=x seq n))
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy

RealPosChar2 [2, 1]
|- all x,n,p(Real x -> all n0(n<=n0 -> (12**p)<=x seq n0) ->
                     RealPos x(PosS p))
   | CauchyElim
   | RealConstrToCauchy

RealPosIntro
|- all x,p((12**p)<=x seq(x mod(PosS p)) -> RealPos x p)

RealPosElim
|- all x,p(RealPos x p -> (12**p)<=x seq(x mod(PosS p)))

RealPosPosS [4, 2]
|- all x,p(Real x -> RealPos x p -> RealPos x(PosS p))
   | CauchyChar1 [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon

RealPosLe [4, 2]
|- all x,y,p(x<<=y -> RealPos x p -> RealPos y(PosS(PosS p)))
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy
   | MonElim
   | RealConstrToMon
   | RealConstrLeElim2

RealPosSemiCompat [2, 3]
|- all x,y,p(x===y -> RealPos x p -> RealPos y(PosS(PosS p)))
   | RealPosLe [4, 2]
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | RealConstrLeElim2
   | RealEqElim0

RealPosToPosAbs
|- all p,x(RealPos x p -> RealPos(abs x)p)

RealPosAbsToPos [2, 2]
|- all x,p(0<<=x -> RealPos abs x p -> RealPos x p)
   | RealConstrNNegElim1
   | RealZeroLeToNNeg [1, 1]
      | RealNNegChar2RealConstrFree

RealLeToPos
|- all x,p((12**p)<<=x -> RealPos x(PosS p))

RealPosToLe [2, 2]
|- all x,p(Real x -> RealPos x p -> (12**PosS p)<<=x)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy

RealPosToZeroLe [3, 3]
|- all x,p(Real x -> RealPos x p -> 0<<=x)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RatLeToRealLe
   | RealPosToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy

RealPlusReal [4, 1]
|- all x,y(Real x -> Real y -> Real(RealPlus x y))
   | CauchyElim
   | CauchyElim
   | MonElim
   | MonElim

NatToRealPlus [1, 4]
|- all n,m RealPlus n m===n+m
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealPosMonPlus [3, 2]
|- all x,y,p,q(Real x -> Real y -> RealPos x p -> RealPos y q ->
                       RealPos(x+y)(PosS(PosS(p min q))))
   | RealPosChar2 [2, 1]
      | CauchyElim
      | RealConstrToCauchy
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy

RealUMinusReal [1, 1]
|- all x(Real x -> Real(~x))
   | CauchyElim

RealUMinusRealInv
|- all x(Real(~ x) -> Real x)

RealAbsReal [2, 1]
|- all x(Real x -> Real(abs x))
   | CauchyElim
   | CauchyElim

RealUDivReal [15, 1]
|- all x,p(Real x -> RealPos abs x p -> Real(RealUDiv x p))
   | CauchyElim
   | RealConstrToCauchy
   | RealConstrToMon
   | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon

RealUDivRealPosFree [12, 1]
|- all x,p(Real x ->
  all n(x mod(PosS p)<=n -> (12**PosS p)<=(abs x)seq n) ->
  Real(RealUDiv x p))
   | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon

RealPosToZeroLeUDiv [5, 2]
|- all x,p(Real x -> RealPos x p -> 0<<=(RealUDiv x p))
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealRat
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealPosToPosAbs
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy

CauchyTimes [2, 1]
|- all as,M,bs,N,p1,p2(
      Cauchy as M -> 
      Cauchy bs N -> 
      Mon M -> 
      Mon N -> 
      all n abs(as n)<=2**p1 -> 
      all n abs(bs n)<=2**p2 -> 
      Cauchy([n]as n*bs n)([p]M(PosS(p+p2))max N(PosS(p+p1))))
   | CauchyElim
   | CauchyElim

RealTimesReal [5, 2]
|- all x,y(Real x -> Real y -> Real(x*y))
   | CauchyTimes [2, 1]
      | CauchyElim
      | CauchyElim
   | RealBdProp [1, 1]
      | CauchyElim
   | RealBdProp [1, 1]
      | CauchyElim
   | MonElim
   | MonElim

RealExpReal [2, 3]
|- all x,n(Real x -> Real(x**n))
   | RealRat
   | RealTimesReal [5, 2]
      | CauchyTimes [2, 1]
         | CauchyElim
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | MonElim
      | MonElim

RealMaxRealAux
|- all as,bs,n,m,p(
 abs(as m+ ~(as n))<=(12**p) ->
 abs(bs n+ ~(bs m))<=(12**p) ->
 as n<=bs n -> abs(as n max bs n+ ~(as m max bs m))<=(12**p))

RealMaxReal [8, 1]
|- all x1,x2(Real x1 -> Real x2 -> Real(x1 max x2))
   | RealMaxRealAux
   | CauchyElim
   | CauchyElim
   | RealMaxRealAux
   | CauchyElim
   | CauchyElim
   | MonElim
   | MonElim

RealMinRealAux
|- all as,bs,n,m,p(
 abs(as n+ ~(as m))<=(12**p) ->
 abs(bs n+ ~(bs m))<=(12**p) ->
 as n<=bs n -> abs(as n min bs n+ ~(as m min bs m))<=(12**p))

RealMinReal [8, 1]
|- all x1,x2(Real x1 -> Real x2 -> Real(x1 min x2))
   | RealMinRealAux
   | CauchyElim
   | CauchyElim
   | RealMinRealAux
   | CauchyElim
   | CauchyElim
   | MonElim
   | MonElim

RatPlusRealPlus [1, 4]
|- all a,b a+b===RealPlus a b
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatUMinusRealUMinus [1, 4]
|- all a ~a===RealUMinus a
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatTimesRealTimes [1, 4]
|- all a,b a*b===RealTimes a b
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatUDivRealUDiv [2, 4]
|- all a,p((12**PosS p)<=abs a ->  RatUDiv a===RealUDiv a p)
   | RealUDivRealPosFree [12, 1]
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatAbsRealAbs [1, 4]
|- all a abs a===RealAbs a
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatExpRealExp [1, 4]
|- all a,n a**n===RealExp a n
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatMaxRealMax [1, 4]
|- all a,b a max b===RealMax a b
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RatMinRealMin [1, 4]
|- all a,b a min b===RealMin a b
   | RealSeqEqToEq [2, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealPlusComm [1, 5]
|- all x,y(Real x -> Real y -> x+y===y+x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealPlusAssoc [1, 5]
|- all x,y,z(Real x -> Real y -> Real z -> x+(y+z)===x+y+z)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealPlusZero [1, 5]
|- all x(Real x -> x+0===x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealZeroPlus [1, 5]
|- all x(Real x -> 0+x===x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealUMinusUMinus [1, 5]
|- all x(Real x -> ~ ~x===x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealUMinusPlus [1, 5]
|- all x,y(Real x -> Real y -> ~(x+y)=== ~x+ ~y)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealUMinusPlusRat [1, 5]
|- all x,k(Real x -> ~(x+k)=== ~x+ ~k)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesComm [1, 5]
|- all x,y(Real x -> Real y -> x*y===y*x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesAssoc [1, 5]
|- all x,y,z(Real x -> Real y -> Real z -> x*(y*z)===x*y*z)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesPlusDistr [1, 5]
|- all x,y,z(Real x -> Real y -> Real z -> x*(y+z)===x*y+x*z)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesPlusDistrLeft [1, 5]
|- all x,y,z(Real x -> Real y -> Real z -> (x+y)*z===x*z+y*z)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesOne [1, 5]
|- all x(Real x -> x*1===x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealOneTimes [1, 5]
|- all x(Real x -> 1*x===x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesIntNOne [1, 5]
|- all x(Real x -> x*IntN 1=== ~x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealIntNOneTimes [1, 5]
|- all x(Real x -> IntN 1*x=== ~x)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesIdUMinus [1, 5]
|- all x,y(Real x -> Real y -> x* ~y=== ~(x*y))
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesIdRatUMinus [1, 5]
|- all x,k(Real x -> x* ~k=== ~(x*k))
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesUDivR [2, 4]
|- all x,p(Real x -> RealPos x p -> x*RealUDiv x p===1)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy

RealTimesUDivRPosFree [4, 4]
|- all x,p(Real x ->
 all n(x mod(PosS p)<=n -> (12**PosS p)<=x seq n) -> x*RealUDiv x p===1)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealTimesReal [5, 2]
      | CauchyTimes [2, 1]
         | CauchyElim
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | MonElim
      | MonElim
   | RealUDivRealPosFree [12, 1]
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealRat

RealTimesUDivR2 [4, 4]
|- all x,p(Real x -> RealPos abs x p -> x*RealUDiv x p===1)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealTimesReal [5, 2]
      | CauchyTimes [2, 1]
         | CauchyElim
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | RealBdProp [1, 1]
         | CauchyElim
      | MonElim
      | MonElim
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealRat

RealTimesUMinusId [1, 5]
|- all x,y(Real x -> Real y -> ~x*y=== ~(x*y))
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealPlusMinusZero [1, 5]
|- all x(Real x -> x+ ~x===0)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealAbsUMinus [1, 5]
|- all x abs abs x eqd abs x
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealAbsUDiv [7, 4]
|- all x,p(Real x -> RealPos x p -> 
                   abs(RealUDiv x p)===RealUDiv(abs x)p)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealPosToPosAbs
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealPosToPosAbs
   | RealPosToPosAbs

RealAbsUDivPosFree [5, 4]
|- all x,p(Real x ->
 all n(x mod(PosS p)<=n -> (12**PosS p)<=x seq n) ->
 abs(RealUDiv x p)===RealUDiv(abs x)p)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim
   | RealUDivRealPosFree [12, 1]
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealUDivRealPosFree [12, 1]
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim

RealUDivUDivReal [4, 1]
|- all x,p,q(Real x -> Real(RealUDiv(RealUDiv x p)q))
   | CauchyElim
   | MonElim
   | MonElim
   | MonElim

RealUDivUDiv [2, 4]
|- all x,p,q(Real x -> RealUDiv(RealUDiv x p)q===x)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealUDivUDivReal [4, 1]
      | CauchyElim
      | MonElim
      | MonElim
      | MonElim

RealTimesPlusIntNOneDistrLeft [1, 5]
|- all k,x(Real x -> (x+IntN 1)* ~k===(x* ~k+k))
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealTimesPlusOneDistrLeft [1, 5]
|- all k,x(Real x -> (x+1)*k===x*k+k)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealLeCompat [4, 3]
|- all x,y,z,z1(x===y -> z===z1 -> x<<=z -> y<<=z1)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealEqElim1
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealEqElim0

RealLeMonPlusR [2, 3]
|- all x,y,z(Real x -> y<<=z -> x+y<<=x+z)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealLeChar1RealConstrFree [1, 2]
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy

RealLeMonPlus [2, 6]
|- all x,y,z(Real x -> y<<=z -> y+x<<=z+x)
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeMonPlusTwo [3, 7]
|- all x,y,z,z0(x<<=y -> z<<=z0 -> x+z<<=y+z0)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlus [2, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy

RealEqCompat [3, 4]
|- all x,y,z,z0(x===y -> z===z0 -> x===z -> y===z0)
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqSym
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1

RealPlusCompat [7, 8]
|- all x,y,z,z0(x===y -> z===z0 -> x+z===y+z0)
   | RealLeAntiSym
   | RealLeMonPlusTwo [3, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
   | RealEqElim0
   | RealEqElim0
   | RealLeMonPlusTwo [3, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
   | RealEqElim1
   | RealEqElim1

RealLePlusL [3, 4]
|- all x,y,z(Real x -> Real z -> y<<= ~x+z -> x+y<<=z)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl

RealLePlusLInv [3, 6]
|- all x,y,z(Real x -> Real y -> x+y<<=z -> y<<= ~x+z)
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLePlusR [2, 4]
|- all x,y,z(Real x -> Real y -> ~y+x<<=z -> x<<=y+z)
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl

RealLePlusRInv [4, 6]
|- all x,y,z(Real y -> Real z -> x<<=y+z -> ~y+x<<=z )
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLePlusUMinus [2, 7]
|- all x,y,z(Real x -> Real y -> Real z -> x+ ~y<<=z -> x+ ~z<<=y)
   | RealLePlusRInv [4, 6]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl

RealLeUMinus [2, 3]
|- all x,y(x<<=y -> ~y<<= ~x)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealLeChar1RealConstrFree [1, 2]
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy

RealLeUMinusInv [7, 6]
|- all x,y(~y<<= ~x -> x<<=y)
   | RealUMinusRealInv
   | RealUMinusRealInv
   | RealLeUMinus [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealEqSym
   | RealUMinusUMinus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqSym
   | RealUMinusUMinus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealUMinusCompat [5, 4]
|- all x,y(x===y -> ~x=== ~y)
   | RealLeAntiSym
   | RealLeUMinus [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealEqElim1
   | RealLeUMinus [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealEqElim0

RealUMinusInj [8, 6]
|- all x,y(~x=== ~y -> x===y)
   | RealUMinusRealInv
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqSym
   | RealUMinusUMinus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealUMinusCompat [5, 4]
      | RealLeAntiSym
      | RealLeUMinus [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqElim1
      | RealLeUMinus [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqElim0
   | RealUMinusUMinus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealUMinusRealInv

RealZeroLeToZeroLeTimes [11, 3]
|- all x,y(0<<=x -> 0<<=y -> 0<<=x*y)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy

RealLeMonTimesR [5, 7]
|- all x,y,z(0<<=x -> y<<=z -> x*y<<=x*z)
   | RealLePlusL [3, 4]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeRefl
   | RealZeroLeToZeroLeTimes [11, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
   | RealLePlusLInv [3, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealEqSym
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeMonTimes [3, 8]
|- all x,y,z(0<<=x -> y<<=z -> y*x<<=z*x)
   | RealLeMonTimesR [5, 7]
      | RealLePlusL [3, 4]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealLeRefl
      | RealZeroLeToZeroLeTimes [11, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
      | RealLePlusLInv [3, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeMonTimesTwo
|- 

RealTimesCompat [9, 6]
|- all x,y,z,z0(x===y -> z===z0 -> x*z===y*z0)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | RealBdPos
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealUDivCompat [3, 4]
|- all x,y,q(x===y -> RealPos abs x q -> RealPos abs y q -> 
                     RealUDiv x q===RealUDiv y q)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealEqChar1
   | RealEqSym

RealAbsCompat [1, 4]
|- all x,y(x===y -> abs x===abs y)
   | RealEqChar2 [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealLeMonExp [7, 9]
|- all x(1<<=x -> all n,m(n<=m -> x**n<<=x**m))
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RatLeToRealLe
   | RatLeToRealLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonTimes [3, 8]
      | RealLeMonTimesR [5, 7]
         | RealLePlusL [3, 4]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealLeRefl
         | RealZeroLeToZeroLeTimes [11, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
         | RealLePlusLInv [3, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | EfRealLe [2, 2]
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
   | RealLeMonTimes [3, 8]
      | RealLeMonTimesR [5, 7]
         | RealLePlusL [3, 4]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealLeRefl
         | RealZeroLeToZeroLeTimes [11, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
         | RealLePlusLInv [3, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim

RealLeMonExpDecr [5, 9]
|- all x(0<<=x -> x<<=1 -> all n,m(n<=m -> x**m<<=x**n))
   | RatLeToRealLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonTimes [3, 8]
      | RealLeMonTimesR [5, 7]
         | RealLePlusL [3, 4]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealLeRefl
         | RealZeroLeToZeroLeTimes [11, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
         | RealLePlusLInv [3, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | EfRealLe [2, 2]
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
      | EfReal [2, 1]
         | EfCauchy
         | EfMon
   | RealLeMonTimes [3, 8]
      | RealLeMonTimesR [5, 7]
         | RealLePlusL [3, 4]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealLeRefl
         | RealZeroLeToZeroLeTimes [11, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
            | RealBdProp [1, 1]
               | CauchyElim
            | RealConstrToCauchy
         | RealLePlusLInv [3, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim

RealExpZeroLe [2, 4]
|- all x(0<<=x -> all n 0<<=x**n)
   | RatLeToRealLe
   | RealZeroLeToZeroLeTimes [11, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy

RealExpLeOne [5, 5]
|- all x(0<<=x -> x<<=1 -> all n x**n<<=1)
   | RatLeToRealLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonTimesTwo
   | RealExpZeroLe [2, 4]
      | RatLeToRealLe
      | RealZeroLeToZeroLeTimes [11, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
   | RatLeToRealLe

RealLeMonExpBase [3, 5]
|- all x,y,n(0<<=x -> x<<=y -> x**n<<=y**n)
   | RatLeToRealLe
   | RealLeMonTimesTwo
   | RealExpZeroLe [2, 4]
      | RatLeToRealLe
      | RealZeroLeToZeroLeTimes [11, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy

RealExpPlus [2, 2]
|- all x,n,m(Real x -> x**(n+m)===x**n *x**m)
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl

RatEqvToRealEq [3, 1]
|- all a,b(a==b -> a===b)
   | RealLeAntiSym
   | RatLeToRealLe
   | RatLeToRealLe

RealEqToRatEqv [4, 1]
|- all a,b(a===b -> a==b)
   | RealLeToRatLe
   | RealEqElim0
   | RealLeToRatLe
   | RealEqElim1

RealExpCompat [2, 7]
|- all x,y,n(x===y -> x**n===y**n)
   | RatEqvToRealEq [3, 1]
      | RealLeAntiSym
      | RatLeToRealLe
      | RatLeToRealLe
   | RealTimesCompat [9, 6]
      | RealEqChar2 [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdPos
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim

RealMaxUB1 [1, 3]
|- all x1,x2(Real x1 -> Real x2 -> x1<<=x1 max x2)
   | RealLeSToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealConstrLeSElim

RealMaxUB2 [1, 3]
|- all x1,x2(Real x1 -> Real x2 -> x2<<=x1 max x2)
   | RealLeSToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealConstrLeSElim

RealMaxLUB [1, 3]
|- all x1,x2,x3(x1<<=x3 -> x2<<=x3 -> x1 max x2<<=x3)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealMaxEq1 [4, 4]
|- all x1,x2(x2<<=x1 -> x1 max x2===x1)
   | RealLeAntiSym
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealMaxEq2 [4, 4]
|- all x1,x2(x1<<=x2 -> x1 max x2===x2)
   | RealLeAntiSym
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealLeMonMax [5, 4]
|- all x1,x2,x3,x4(x1<<=x2 -> x3<<=x4 -> x1 max x3<<=x2 max x4)
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealMaxAssoc [19, 4]
|- all x1,x2,x3(Real x1 -> Real x2 -> Real x3 ->
 x1 max(x2 max x3)===x1 max x2 max x3)
   | RealLeAntiSym
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealMaxCompat [7, 5]
|- all x1,x2,x3,x4(x1===x2 -> x3===x4 -> x1 max x3===x2 max x4)
   | RealLeAntiSym
   | RealLeMonMax [5, 4]
      | RealMaxLUB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMaxUB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMaxUB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealLeRefl
   | RealLeRefl
   | RealLeMonMax [5, 4]
      | RealMaxLUB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMaxUB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMaxUB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealLeRefl
   | RealLeRefl

RealMinLB1 [1, 3]
|- all x1,x2(Real x1 -> Real x2 -> x1 min x2<<=x1)
   | RealLeSToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealConstrLeSElim

RealMinLB2 [1, 3]
|- all x1,x2(Real x1 -> Real x2 -> x1 min x2<<=x2)
   | RealLeSToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealConstrLeSElim

RealMinGLB [1, 3]
|- all x1,x2,x3(x3<<=x1 -> x3<<=x2 -> x3<<=x1 min x2)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealMinEq1 [4, 4]
|- all x,y(x<<=y -> x min y===x)
   | RealLeAntiSym
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl

RealMinEq2 [4, 4]
|- all x,y(y<<=x -> x min y===y)
   | RealLeAntiSym
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeRefl

RealLeMonMin [5, 4]
|- all x1,x2,x3,x4(x1<<=x2 -> x3<<=x4 -> x1 min x3<<=x2 min x4)
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealMinAssoc [17, 5]
|- all x1,x2,x3(Real x1 -> Real x2 -> Real x3 ->
  x1 min(x2 min x3)===x1 min x2 min x3)
   | RealLeAntiSym
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeMonMin [5, 4]
      | RealMinGLB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealLeRefl
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonMin [5, 4]
      | RealMinGLB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealLeRefl
   | RealLeRefl

RealMinComm [7, 4]
|- all x1,x2(Real x1 -> Real x2 -> x1 min x2===x2 min x1)
   | RealLeAntiSym
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinGLB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealMinLB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMinLB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim

RealMinCompat [7, 5]
|- all x1,x2,x3,x4(x1===x2 -> x3===x4 -> x1 min x3===x2 min x4)
   | RealLeAntiSym
   | RealLeMonMin [5, 4]
      | RealMinGLB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealLeRefl
   | RealLeRefl
   | RealLeMonMin [5, 4]
      | RealMinGLB [1, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB1 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealMinLB2 [1, 3]
         | RealLeSToLe [2, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealConstrLeSElim
   | RealLeRefl
   | RealLeRefl

RealLeToNNeg [2, 7]
|- all x,y(x<<=y -> RealNNeg(~x+y))
   | RealZeroLeToNNeg [1, 1]
      | RealNNegChar2RealConstrFree
   | RealLePlusLInv [3, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim

RealNNegToLe [4, 6]
|- all x,y(Real x -> Real y -> RealNNeg(~x+y) -> x<<=y)
   | RealLePlusL [3, 4]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeRefl
   | RealNNegToZeroLe [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealEqSym
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeAbs [1, 3]
|- all x,y(x<<=y -> ~x<<=y -> abs x<<=y)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealLeIdAbs [1, 3]
|- all x(Real x -> x<<=abs x)
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealLeAbsInv [3, 4]
|- all x,y(Real x -> abs x<<=y -> ~y<<=x)
   | RealLeUMinus [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealLeAbsPlus [6, 3]
|- all x,y(Real x -> Real y -> abs(x+y)<<=abs x+abs y)
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim
   | RealPlusReal [4, 1]
      | CauchyElim
      | CauchyElim
      | MonElim
      | MonElim
   | RealPlusReal [4, 1]
      | CauchyElim
      | CauchyElim
      | MonElim
      | MonElim
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim
   | RealAbsReal [2, 1]
      | CauchyElim
      | CauchyElim

RealAbsTimes [1, 5]
|- all x,y(Real x -> Real y -> abs(x*y)===abs x*abs y)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealLeAbsId [1, 3]
|- all x(0<<=x -> abs x<<=x)
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealEqAbsId [2, 4]
|- all x(0<<=x -> abs x===x)
   | RealLeAbsId [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealAbsZero [6, 7]
|- all x abs abs x eqd abs x
   | RealLeAntiSym
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeUMinusInv [7, 6]
      | RealUMinusRealInv
      | RealUMinusRealInv
      | RealLeUMinus [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSym
      | RealUMinusUMinus [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqSym
      | RealUMinusUMinus [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RatLeToRealLe

RealLeZeroAbs [1, 3]
|- all x(Real x -> 0<<=abs x)
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealAbsExp [3, 2]
|- all x,n(Real x -> abs(x**n)===abs x**n)
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealRat
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl

RealAbsMax [7, 4]
|- all x(Real x -> abs x===x max~x)
   | RealLeAntiSym
   | RealLeAbs [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealMaxUB1 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxUB2 [1, 3]
      | RealLeSToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealConstrLeSElim
   | RealMaxLUB [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealLeUDivUDiv [13, 3]
|- all x,y,p,q((12**p)<<=x -> (12**q)<<=y -> x<<=y ->
 RealUDiv y(PosS q)<<=RealUDiv x(PosS p))
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealPosToPosAbs
   | RealLeToPos
   | RealUDivReal [15, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrToMon
      | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
   | RealPosToPosAbs
   | RealLeToPos
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealLeToPos
   | RealLeToPos
   | CauchyElim
   | RealConstrToCauchy
   | CauchyElim
   | RealConstrToCauchy

RealLeUDivUDivInv [3, 5]
|- all x,y,p,q,p1,q1(Real x -> Real y ->
 (12**p)<<=RealUDiv x p1 -> 
 (12**q)<<=RealUDiv y q1 ->
 RealUDiv x p1<<=RealUDiv y q1 -> y<<=x)
   | RealLeUDivUDiv [13, 3]
      | RealUDivReal [15, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrToMon
         | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
      | RealPosToPosAbs
      | RealLeToPos
      | RealUDivReal [15, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrToMon
         | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
      | RealPosToPosAbs
      | RealLeToPos
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeToPos
      | RealLeToPos
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealUDivUDiv [2, 4]
      | RealEqChar2 [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealUDivUDivReal [4, 1]
         | CauchyElim
         | MonElim
         | MonElim
         | MonElim
   | RealUDivUDiv [2, 4]
      | RealEqChar2 [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealUDivUDivReal [4, 1]
         | CauchyElim
         | MonElim
         | MonElim
         | MonElim

RealLeUDiv [12, 4]
|- all x,p,y,q(Real x -> RealPos x p -> Real y -> RealPos y q ->
 RealUDiv x p<<=y -> RealUDiv y q<<=x)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonTimesTwo
   | RatLeToRealLe
   | RealPosToZeroLeUDiv [5, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealRat
      | RealUDivReal [15, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrToMon
         | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
      | RealPosToPosAbs
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonTimesTwo
   | RealPosToZeroLe [3, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RatLeToRealLe
      | RealPosToLe [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealPosChar1 [2, 1]
            | CauchyElim
            | RealConstrToCauchy
   | RealPosToZeroLeUDiv [5, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealRat
      | RealUDivReal [15, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrToMon
         | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
      | RealPosToPosAbs
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl
   | RealLeRefl
   | RealLeRefl

RealApprox [8, 1]
|- all x,p(Real x -> exl a abs(a+ ~x)<<=(12**p))
   | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon
   | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon

RealTimesZero [1, 5]
|- all x(Real x -> x*0===0)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealZeroTimes [1, 5]
|- all x(Real x -> 0*x===0)
   | RealEqSToEq [2, 4]
      | RealSeqEqToEq [2, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
      | RealEqSElim

RealLeZeroSquare [1, 3]
|- all x(Real x -> 0<<=x*x)
   | RealSeqLeToLe [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy

RealEqPlusMinus [2, 6]
|- all x,y(Real x -> Real y -> x+ ~y+y===x)
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealPlusInsert [4, 9]
|- all x,y,z(Real x -> Real y -> Real z -> x+z===x+ ~y+(y+z))
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPlusMinusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

ApproxSplitPos [6, 2]
|- all x,y,z,p(Real x -> Real y -> Real z -> RealPos(y+ ~x)p ->
                       z<<=y oru x<<=z)
   | CauchyElim
   | RealConstrToCauchy
   | CauchyElim
   | RealConstrToCauchy
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy

RealLtIntro
|- all x,y,p(RealPos(y+ ~x)p -> RealLt x y p)

RealLtElim
|- all x,y,p(RealLt x y p -> RealPos(y+ ~x)p)

RealNotPosToLe [3, 2]
|- all x(Real x -> all p(RealPos x p -> F) -> x<<=0)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | CauchyChar1 [1, 1]
      | CauchyElim
   | RealConstrToCauchy

RealNotLtToLe [5, 6]
|- all x,y(Real x -> Real y -> all p(RealLt y x p -> F) -> x<<=y)
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealNotPosToLe [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | CauchyChar1 [1, 1]
         | CauchyElim
      | RealConstrToCauchy
   | RealLtIntro
   | RealEqSym
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

ApproxSplit [2, 3]
|- all x,y,z,p(Real x -> Real y -> Real z -> RealLt x y p ->
                       z<<=y oru x<<=z)
   | ApproxSplitPos [6, 2]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | RealLtElim

RealAllncTotalIntro
|- allnc as,M (Pvar rea)(RealConstr as M) -> allnc x (Pvar rea)x

RealAllncTotalElim
|- allnc x (Pvar rea)x -> allnc as,M (Pvar rea)(RealConstr as M)

RealLePlusCancelL [2, 2]
|- all x,y,z(Real x -> Real y -> Real z -> x+y<<=x+z -> y<<=z)
   | RealLeChar2 [4, 1]
      | CauchyElim
      | RealConstrToCauchy
      | CauchyElim
      | RealConstrToCauchy
   | RealLeChar1 [5, 1]
      | CauchyElim
      | RealConstrToCauchy
      | RealConstrLeElim2
      | CauchyElim
      | RealConstrToCauchy

RealLePlusCancelR [3, 6]
|- all x,y,z(Real x -> Real y -> Real z -> x+y<<=z+y -> x<<=z)
   | RealLePlusCancelL [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealEqPlusCancelL [5, 3]
|- all x,y,z(Real x -> Real y -> Real z -> x+y===x+z -> y===z)
   | RealLeAntiSym
   | RealLePlusCancelL [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl
   | RealLePlusCancelL [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl

RealEqPlusCancelR [3, 6]
|- all x,y,z(Real x -> Real y -> Real z -> x+z===y+z -> x===y)
   | RealEqPlusCancelL [5, 3]
      | RealLeAntiSym
      | RealLePlusCancelL [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeRefl
      | RealLePlusCancelL [2, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeRefl
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeTimesCancelL [9, 7]
|- all x,y,z,p(Real x -> Real y -> Real z -> RealPos x p ->
 x*y<<=x*z -> y<<=z)
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl
   | RealLePlusL [3, 4]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealZeroLeToZeroLeTimes [11, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | RealBdProp [1, 1]
         | CauchyElim
      | RealConstrToCauchy
   | RealPosToZeroLeUDiv [5, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealRat
      | RealUDivReal [15, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrToMon
         | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
      | RealPosToPosAbs
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
   | RealLePlusLInv [3, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeRefl
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeTimesCancelR [3, 8]
|- all x,y,z,p(Real x -> Real y -> Real z -> RealPos y p ->
 x*y<<=z*y -> x<<=z)
   | RealLeTimesCancelL [9, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeRefl
      | RealLePlusL [3, 4]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealLeRefl
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealZeroLeToZeroLeTimes [11, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
      | RealPosToZeroLeUDiv [5, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealRat
         | RealUDivReal [15, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrToMon
            | CauchyElim
            | RealConstrToCauchy
            | MonElim
            | RealConstrToMon
            | MonElim
            | RealConstrToMon
            | MonElim
            | RealConstrToMon
            | MonElim
            | RealConstrToMon
            | MonElim
            | RealConstrToMon
         | RealPosToPosAbs
         | RealPosChar1 [2, 1]
            | CauchyElim
            | RealConstrToCauchy
      | RealLePlusLInv [3, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeRefl
      | RealTimesComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealEqTimesCancelL
|- 

RealEqTimesCancelR
|- 

RealLeAllPlusToLe [4, 6]
|- all x,y(Real x -> Real y -> all p x<<=y+(12**p) -> x<<=y)
   | RealEqSym
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqSym
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeAllAbsToEq [9, 7]
|- all x,y(Real x -> Real y -> all p abs(x+ ~y)<<=(12**p) -> x===y)
   | RealLeAntiSym
   | RealLeAllPlusToLe [4, 6]
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeAllPlusToLe [4, 6]
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealLePlusL [3, 4]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeRefl
   | RealLeAbsInv [3, 4]
      | RealLeUMinus [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeIdAbs [1, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy

RealPlusHalfExpPosS [1, 2]
|- all p RealPlus(12**PosS p)(12**PosS p)===(12**p)
   | RatEqvToRealEq [3, 1]
      | RealLeAntiSym
      | RatLeToRealLe
      | RatLeToRealLe

RealPosPlus [9, 2]
|- all x,y,p(
 0<<=x -> Real y -> RealPos y p -> RealPos(x+y)(PosS(PosS p)))
   | CauchyChar1 [1, 1]
      | CauchyElim
   | RealConstrToCauchy
   | MonElim
   | RealConstrToMon
   | MonElim
   | RealConstrToMon
   | RealPosChar1 [2, 1]
      | CauchyElim
      | RealConstrToCauchy
   | MonElim
   | RealConstrToMon

RealLeAbsMinus1 [3, 5]
|- all x,y,z(Real x -> Real y -> abs(x+ ~y)<<=z -> x<<=y+z)
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealAbsPlusUMinus [1, 2]
|- all x,y(Real x -> Real y -> abs(x+ ~y)===abs(y+ ~x))
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl

RealLeAbsMinus2 [3, 5]
|- all x,y,z(Real x -> Real y -> abs(x+ ~y)<<=z -> y<<=x+z)
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeIdAbs [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy

RealLeAbsMinus [5, 6]
|- all x,y,z (Real x -> Real y -> Real z ->
 abs(x+ ~y) <<= abs(x+ ~z)+abs(z+ ~y))
   | RealLeAbsPlus [6, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
      | RealPlusReal [4, 1]
         | CauchyElim
         | CauchyElim
         | MonElim
         | MonElim
      | RealPlusReal [4, 1]
         | CauchyElim
         | CauchyElim
         | MonElim
         | MonElim
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqSym
   | RealPlusAssoc [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLeMinusAbs [31, 9]
|- all x,y(Real x -> Real y -> abs x+ ~abs y<<=abs(x+ ~y))
   | RealLeCompat [4, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealAbsCompat [1, 4]
      | RealEqChar2 [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqSym
   | RealPlusAssoc [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusMinusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlusTwo [3, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
   | RealLeAbsPlus [6, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
      | RealPlusReal [4, 1]
         | CauchyElim
         | CauchyElim
         | MonElim
         | MonElim
      | RealPlusReal [4, 1]
         | CauchyElim
         | CauchyElim
         | MonElim
         | MonElim
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
      | RealAbsReal [2, 1]
         | CauchyElim
         | CauchyElim
   | RealLeRefl
   | RealLeCompat [4, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
   | RealEqSym
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqSym
   | RealPlusAssoc [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPlusMinusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealLeRefl

RealLeAbsMinusAbs [13, 10]
|- all x,y(Real x -> Real y -> abs(abs x+ ~abs y)<<=abs(x+ ~y))
   | RealLeAbs [1, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RealLeMinusAbs [31, 9]
      | RealLeCompat [4, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealAbsCompat [1, 4]
         | RealEqChar2 [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqSym
      | RealPlusAssoc [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusMinusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealLeAbsPlus [6, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
         | RealPlusReal [4, 1]
            | CauchyElim
            | CauchyElim
            | MonElim
            | MonElim
         | RealPlusReal [4, 1]
            | CauchyElim
            | CauchyElim
            | MonElim
            | MonElim
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
      | RealLeRefl
      | RealLeCompat [4, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
      | RealEqSym
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqSym
      | RealPlusAssoc [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusMinusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealLeRefl
   | RealLeCompat [4, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
   | RealEqSym
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealUMinusPlus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqTrans [6, 3]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealPlusComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealUMinusUMinus [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealAbsPlusUMinus [1, 2]
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealLeMinusAbs [31, 9]
      | RealLeCompat [4, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealAbsCompat [1, 4]
         | RealEqChar2 [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqSym
      | RealPlusAssoc [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusMinusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealLeAbsPlus [6, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
         | RealPlusReal [4, 1]
            | CauchyElim
            | CauchyElim
            | MonElim
            | MonElim
         | RealPlusReal [4, 1]
            | CauchyElim
            | CauchyElim
            | MonElim
            | MonElim
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
         | RealAbsReal [2, 1]
            | CauchyElim
            | CauchyElim
      | RealLeRefl
      | RealLeCompat [4, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
      | RealEqSym
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqSym
      | RealPlusAssoc [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqTrans [6, 3]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusMinusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealLeRefl

RealLeTransRat [2, 3]
|- all a,x,b(a<<=x -> x<<=b -> a<=b)
   | RealLeToRatLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy

RealLeBound [4, 3]
|- all x(Real x -> x<<=2**(cRBd(x seq)(x mod)))
   | RealLeSToLe [2, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealConstrLeSElim
   | RealRat
   | RealBdProp [1, 1]
      | CauchyElim
   | RealConstrToCauchy

RatCauchyConvMod [3, 3]
|- all as,M,p,n(Real(RealConstr as M) -> M p<=n ->
                        abs(as n+ ~(RealConstr as M))<<=(12**p))
   | RealLeChar2RealConstrFree [1, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
   | CauchyElim
   | RealConstrToCauchy

RatCauchyConvModRealConstrFree
|- 

RealLeExpBernoulli [20, 8]
|- all x,n(~1<<=x -> 1+n*x<<=(1+x)**n)
   | RatLeToRealLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlusTwo [3, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
   | RatLeToRealLe
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeRefl
   | RealLeMonPlusTwo [3, 7]
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
   | RealLeRefl
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RatLeToRealLe
   | RealLeMonTimesTwo
   | RatLeToRealLe
   | RatLeToRealLe
   | RatLeToRealLe
   | RealLeZeroSquare [1, 3]
      | RealSeqLeToLe [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
   | RatEqvToRealEq [3, 1]
      | RealLeAntiSym
      | RatLeToRealLe
      | RatLeToRealLe
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealLeMonTimesR [5, 7]
      | RealLePlusL [3, 4]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealLeRefl
      | RealZeroLeToZeroLeTimes [11, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | RealBdProp [1, 1]
            | CauchyElim
         | RealConstrToCauchy
      | RealLePlusLInv [3, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLePlusR [2, 4]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
   | RealTimesComm [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim

RealLtIrrefl [2, 6]
|- all x,p(Real x -> RealLt x x p -> F)
   | RealPlusMinusZero [1, 5]
      | RealEqSToEq [2, 4]
         | RealSeqEqToEq [2, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqSElim
   | RealLtElim

RealLtLeTrans [8, 9]
|- all x,y,z,p(Real x ->
 RealLt x y p -> y<<=z -> RealLt x z(PosS(PosS(PosS(PosS p)))))
   | RealLtIntro
   | RealPosSemiCompat [2, 3]
      | RealPosLe [4, 2]
         | RealPosChar1 [2, 1]
            | CauchyElim
            | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | RealConstrLeElim2
      | RealEqElim0
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPosPlus [9, 2]
      | CauchyChar1 [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
   | RealLePlusLInv [3, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLtElim

RealLeLtTrans [8, 9]
|- all x,y,z,p(Real z ->
 x<<=y -> RealLt y z p -> RealLt x z(PosS(PosS(PosS(PosS p)))))
   | RealLtIntro
   | RealPosSemiCompat [2, 3]
      | RealPosLe [4, 2]
         | RealPosChar1 [2, 1]
            | CauchyElim
            | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | RealConstrLeElim2
      | RealEqElim0
   | RealPlusCompat [7, 8]
      | RealLeAntiSym
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim0
      | RealEqElim0
      | RealLeMonPlusTwo [3, 7]
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeMonPlus [2, 6]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealPlusComm [1, 5]
               | RealEqSToEq [2, 4]
                  | RealSeqEqToEq [2, 3]
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                     | RealSeqLeToLe [1, 2]
                        | RealLeChar2 [4, 1]
                           | CauchyElim
                           | RealConstrToCauchy
                           | CauchyElim
                           | RealConstrToCauchy
                  | RealEqSElim
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
      | RealEqElim1
      | RealEqElim1
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealEqRefl [2, 1]
      | RealLeRefl
      | RealLeRefl
   | RealPosPlus [9, 2]
      | CauchyChar1 [1, 1]
         | CauchyElim
      | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
      | MonElim
      | RealConstrToMon
      | RealPosChar1 [2, 1]
         | CauchyElim
         | RealConstrToCauchy
      | MonElim
      | RealConstrToMon
   | RealLePlusLInv [3, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLtElim

RealLeToNotLt [2, 10]
|- all x,y,p(x<<=y -> RealLt y x p -> F)
   | RealLtIrrefl [2, 6]
      | RealPlusMinusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealLtElim
   | RealLeLtTrans [8, 9]
      | RealLtIntro
      | RealPosSemiCompat [2, 3]
         | RealPosLe [4, 2]
            | RealPosChar1 [2, 1]
               | CauchyElim
               | RealConstrToCauchy
            | MonElim
            | RealConstrToMon
            | RealConstrLeElim2
         | RealEqElim0
      | RealPlusCompat [7, 8]
         | RealLeAntiSym
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim0
         | RealEqElim0
         | RealLeMonPlusTwo [3, 7]
            | RealLeTrans [3, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeMonPlus [2, 6]
               | RealLeMonPlusR [2, 3]
                  | RealLeChar2RealConstrFree [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealLeChar1RealConstrFree [1, 2]
                     | RealLeChar1 [5, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | RealConstrLeElim2
                        | CauchyElim
                        | RealConstrToCauchy
               | RealPlusComm [1, 5]
                  | RealEqSToEq [2, 4]
                     | RealSeqEqToEq [2, 3]
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                        | RealSeqLeToLe [1, 2]
                           | RealLeChar2 [4, 1]
                              | CauchyElim
                              | RealConstrToCauchy
                              | CauchyElim
                              | RealConstrToCauchy
                     | RealEqSElim
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
         | RealEqElim1
         | RealEqElim1
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealEqRefl [2, 1]
         | RealLeRefl
         | RealLeRefl
      | RealPosPlus [9, 2]
         | CauchyChar1 [1, 1]
            | CauchyElim
         | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
         | MonElim
         | RealConstrToMon
         | RealPosChar1 [2, 1]
            | CauchyElim
            | RealConstrToCauchy
         | MonElim
         | RealConstrToMon
      | RealLePlusLInv [3, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLtElim

RatLtToRealLt
|- all a,b(a<b -> exl p RealLt a b p)

RealConvElim1
|- all xs,x,M(RealConv xs x M -> all n Real(xs n))

RealConvElim2
|- all xs,x,M(RealConv xs x M -> Real x)

RealConvElim3
|- all xs,x,M(RealConv xs x M -> Mon M)

RealConvElim4
|- all xs,x,M(RealConv xs x M -> all p,n(M p<=n ->
 abs(xs n+ ~x)<<=(12**p)))

RealConvLe [12, 7]
|- all x,y,xs,ys,M,N(
 all n xs n<<=ys n -> RealConv xs x M -> RealConv ys y N -> x<<=y)
   | RealLeAllPlusToLe [4, 6]
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
      | RealEqSym
      | RealPlusZero [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeAbsMinus2 [3, 5]
      | RealLePlusR [2, 4]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeIdAbs [1, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
   | RealConvElim4
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlus [2, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeTrans [3, 2]
      | RealLeChar2 [4, 1]
         | CauchyElim
         | RealConstrToCauchy
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
      | RealLeChar1 [5, 1]
         | CauchyElim
         | RealConstrToCauchy
         | RealConstrLeElim2
         | CauchyElim
         | RealConstrToCauchy
   | RealLeMonPlus [2, 6]
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RealPlusComm [1, 5]
         | RealEqSToEq [2, 4]
            | RealSeqEqToEq [2, 3]
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealSeqLeToLe [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqSElim
   | RealLeAbsMinus1 [3, 5]
      | RealLePlusR [2, 4]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealEqRefl [2, 1]
            | RealLeRefl
            | RealLeRefl
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeIdAbs [1, 3]
         | RealSeqLeToLe [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
   | RealConvElim4
   | RealLeMonPlusR [2, 3]
      | RealLeChar2RealConstrFree [1, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
      | RealLeChar1RealConstrFree [1, 2]
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
   | RatLeToRealLe

RealConvEq
|- 

RealConvEq [5, 8]
|- all x,y,xs,ys,M,N(
 all n xs n===ys n -> RealConv xs x M -> RealConv ys y N -> x===y)
   | RealLeAntiSym
   | RealConvLe [12, 7]
      | RealLeAllPlusToLe [4, 6]
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeAbsMinus2 [3, 5]
         | RealLePlusR [2, 4]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeIdAbs [1, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealConvElim4
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeAbsMinus1 [3, 5]
         | RealLePlusR [2, 4]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeIdAbs [1, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealConvElim4
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RatLeToRealLe
   | RealEqElim0
   | RealConvLe [12, 7]
      | RealLeAllPlusToLe [4, 6]
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
         | RealEqSym
         | RealPlusZero [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeAbsMinus2 [3, 5]
         | RealLePlusR [2, 4]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeIdAbs [1, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealConvElim4
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeTrans [3, 2]
         | RealLeChar2 [4, 1]
            | CauchyElim
            | RealConstrToCauchy
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
         | RealLeChar1 [5, 1]
            | CauchyElim
            | RealConstrToCauchy
            | RealConstrLeElim2
            | CauchyElim
            | RealConstrToCauchy
      | RealLeMonPlus [2, 6]
         | RealLeMonPlusR [2, 3]
            | RealLeChar2RealConstrFree [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
            | RealLeChar1RealConstrFree [1, 2]
               | RealLeChar1 [5, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | RealConstrLeElim2
                  | CauchyElim
                  | RealConstrToCauchy
         | RealPlusComm [1, 5]
            | RealEqSToEq [2, 4]
               | RealSeqEqToEq [2, 3]
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
                  | RealSeqLeToLe [1, 2]
                     | RealLeChar2 [4, 1]
                        | CauchyElim
                        | RealConstrToCauchy
                        | CauchyElim
                        | RealConstrToCauchy
               | RealEqSElim
      | RealLeAbsMinus1 [3, 5]
         | RealLePlusR [2, 4]
            | RealLeMonPlusR [2, 3]
               | RealLeChar2RealConstrFree [1, 2]
                  | RealLeChar2 [4, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | CauchyElim
                     | RealConstrToCauchy
               | RealLeChar1RealConstrFree [1, 2]
                  | RealLeChar1 [5, 1]
                     | CauchyElim
                     | RealConstrToCauchy
                     | RealConstrLeElim2
                     | CauchyElim
                     | RealConstrToCauchy
            | RealEqRefl [2, 1]
               | RealLeRefl
               | RealLeRefl
         | RealLeTrans [3, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
         | RealLeIdAbs [1, 3]
            | RealSeqLeToLe [1, 2]
               | RealLeChar2 [4, 1]
                  | CauchyElim
                  | RealConstrToCauchy
                  | CauchyElim
                  | RealConstrToCauchy
      | RealConvElim4
      | RealLeMonPlusR [2, 3]
         | RealLeChar2RealConstrFree [1, 2]
            | RealLeChar2 [4, 1]
               | CauchyElim
               | RealConstrToCauchy
               | CauchyElim
               | RealConstrToCauchy
         | RealLeChar1RealConstrFree [1, 2]
            | RealLeChar1 [5, 1]
               | CauchyElim
               | RealConstrToCauchy
               | RealConstrLeElim2
               | CauchyElim
               | RealConstrToCauchy
      | RatLeToRealLe
   | RealEqElim1