Goal:
  
  __p2 : Prop
  __p1 : Prop
  __x4 : BinNums.Z
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  __wit := [ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC
                       (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                       (RingMicromega.PsatzIn BinNums.Z 2))
                    (RingMicromega.PsatzIn BinNums.Z 0)))
              ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd
                 (RingMicromega.PsatzMulC
                    (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                    (RingMicromega.PsatzIn BinNums.Z 3))
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                    (RingMicromega.PsatzIn BinNums.Z 0)))
              ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 1)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC
                       (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                       (RingMicromega.PsatzIn BinNums.Z 4))
                    (RingMicromega.PsatzAdd
                       (RingMicromega.PsatzIn BinNums.Z 2)
                       (RingMicromega.PsatzIn BinNums.Z 0))))
              ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
                    (RingMicromega.PsatzAdd
                       (RingMicromega.PsatzMulC
                          (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                          (RingMicromega.PsatzIn BinNums.Z 2))
                       (RingMicromega.PsatzIn BinNums.Z 0))))
              ZMicromega.DoneProof] : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
                (VarMap.Elt __x3) : VarMap.t BinNums.Z
  __ff := Tauto.IMPL
            (Tauto.OR
               (Tauto.AND
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEc BinNums.Z0;
                       RingMicromega.Fop := RingMicromega.OpLt;
                       RingMicromega.Frhs :=
                         EnvRing.PEsub (EnvRing.PEX (BinNums.xI BinNums.xH))
                           (EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH)))
                     |} tt)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs :=
                         EnvRing.PEsub (EnvRing.PEX (BinNums.xI BinNums.xH))
                           (EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH)))
                     |} tt))
               (Tauto.AND
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs :=
                         EnvRing.PEsub (EnvRing.PEX (BinNums.xI BinNums.xH))
                           (EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH)));
                       RingMicromega.Fop := RingMicromega.OpLe;
                       RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                     |} tt) (Tauto.X Tauto.isProp __p1))) None
            (Tauto.IMPL
               (Tauto.OR
                  (Tauto.AND (Tauto.X Tauto.isProp __p2)
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEX (BinNums.xO BinNums.xH);
                          RingMicromega.Fop := RingMicromega.OpEq;
                          RingMicromega.Frhs :=
                            EnvRing.PEsub
                              (EnvRing.PEX (BinNums.xI BinNums.xH))
                              (EnvRing.PEadd
                                 (EnvRing.PEX
                                    (BinNums.xO (BinNums.xO BinNums.xH)))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                        |} tt))
                  (Tauto.AND
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEsub
                              (EnvRing.PEX (BinNums.xI BinNums.xH))
                              (EnvRing.PEadd
                                 (EnvRing.PEX
                                    (BinNums.xO (BinNums.xO BinNums.xH)))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH)));
                          RingMicromega.Fop := RingMicromega.OpLe;
                          RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                        |} tt)
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEX (BinNums.xO BinNums.xH);
                          RingMicromega.Fop := RingMicromega.OpEq;
                          RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                        |} tt))) None
               (Tauto.IMPL
                  (Tauto.NOT
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEX (BinNums.xI BinNums.xH);
                          RingMicromega.Fop := RingMicromega.OpLt;
                          RingMicromega.Frhs :=
                            EnvRing.PEadd
                              (EnvRing.PEX
                                 (BinNums.xO (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.OpEq;
                       RingMicromega.Frhs :=
                         EnvRing.PEadd (EnvRing.PEX (BinNums.xO BinNums.xH))
                           (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                     |} tt)))
       : Tauto.BFormula (RingMicromega.Formula BinNums.Z) Tauto.isProp
  ============================
   (BinInt.Z.lt BinNums.Z0 (BinInt.Z.sub __x3 __x4)
    ∧ __x1 = BinInt.Z.sub __x3 __x4
    ∨ BinInt.Z.le (BinInt.Z.sub __x3 __x4) BinNums.Z0 ∧ __p1
    → __p2
      ∧ __x2 =
        BinInt.Z.sub __x3 (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH))
      ∨ BinInt.Z.le
          (BinInt.Z.sub __x3 (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH)))
          BinNums.Z0 ∧ __x2 = BinNums.Z0
      → (BinInt.Z.lt __x3 (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH))
         → False) → __x1 = BinInt.Z.add __x2 (BinNums.Zpos BinNums.xH))


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