Goal:
  
  __p2 : Prop
  __p1 : Prop
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  __wit := [ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                    (RingMicromega.PsatzAdd
                       (RingMicromega.PsatzIn BinNums.Z 1)
                       (RingMicromega.PsatzIn BinNums.Z 0))))
              ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                    (RingMicromega.PsatzIn BinNums.Z 0)))
              ZMicromega.DoneProof] : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch (VarMap.Elt __x2) __x1 (VarMap.Elt __x3)
           : VarMap.t BinNums.Z
  __ff := Tauto.IMPL
            (Tauto.OR
               (Tauto.AND (Tauto.X Tauto.isProp __p1)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs :=
                         EnvRing.PEsub (EnvRing.PEX (BinNums.xO BinNums.xH))
                           (EnvRing.PEadd
                              (EnvRing.PEX (BinNums.xI BinNums.xH))
                              (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                     |} tt))
               (Tauto.AND (Tauto.X Tauto.isProp __p2)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                     |} tt))) None
            (Tauto.IMPL
               (Tauto.A Tauto.isProp
                  {|
                    RingMicromega.Flhs := EnvRing.PEc BinNums.Z0;
                    RingMicromega.Fop := RingMicromega.OpLe;
                    RingMicromega.Frhs := EnvRing.PEX (BinNums.xI BinNums.xH)
                  |} tt) None
               (Tauto.IMPL
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs :=
                         EnvRing.PEadd (EnvRing.PEX (BinNums.xI BinNums.xH))
                           (EnvRing.PEc (BinNums.Zpos BinNums.xH));
                       RingMicromega.Fop := RingMicromega.OpLt;
                       RingMicromega.Frhs :=
                         EnvRing.PEadd (EnvRing.PEX (BinNums.xO BinNums.xH))
                           (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                     |} tt) None
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                       RingMicromega.Fop := RingMicromega.OpLt;
                       RingMicromega.Frhs :=
                         EnvRing.PEX (BinNums.xO BinNums.xH)
                     |} tt)))
       : Tauto.BFormula (RingMicromega.Formula BinNums.Z) Tauto.isProp
  ============================
   (__p1
    ∧ __x1 = BinInt.Z.sub __x2 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
    ∨ __p2 ∧ __x1 = BinNums.Z0
    → BinInt.Z.le BinNums.Z0 __x3
      → BinInt.Z.lt (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
          (BinInt.Z.add __x2 (BinNums.Zpos BinNums.xH))
        → BinInt.Z.lt __x1 __x2)


DEBUG:Going to execute:
exact
(ZMicromega.ZTautoChecker_sound __ff __wit
   (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
   (VarMap.find BinNums.Z0 __varmap))