Goal:
  
  __x5 : BinNums.Z
  __x4 : BinNums.Z
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  __wit := [ZMicromega.RatProof
              (RingMicromega.PsatzAdd
                 (RingMicromega.PsatzMulC
                    (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                    (RingMicromega.PsatzIn BinNums.Z 3))
                 (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.PsatzMulC
                       (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                       (RingMicromega.PsatzIn BinNums.Z 1))
                    (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 1)
                    (RingMicromega.PsatzIn BinNums.Z 0)))
              ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC
                       (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                       (RingMicromega.PsatzIn BinNums.Z 1))
                    (RingMicromega.PsatzIn BinNums.Z 0)))
              ZMicromega.DoneProof] : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
                (VarMap.Branch (VarMap.Elt __x5) __x3 VarMap.Empty)
           : 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.PEadd
                              (EnvRing.PEX
                                 (BinNums.xO (BinNums.xO BinNums.xH)))
                              (EnvRing.PEadd
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH)))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH))))
                           (EnvRing.PEadd
                              (EnvRing.PEX (BinNums.xI BinNums.xH))
                              (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                     |} tt)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs :=
                         EnvRing.PEsub
                           (EnvRing.PEadd
                              (EnvRing.PEX
                                 (BinNums.xO (BinNums.xO BinNums.xH)))
                              (EnvRing.PEadd
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH)))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH))))
                           (EnvRing.PEadd
                              (EnvRing.PEX (BinNums.xI BinNums.xH))
                              (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                     |} tt))
               (Tauto.AND
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs :=
                         EnvRing.PEsub
                           (EnvRing.PEadd
                              (EnvRing.PEX
                                 (BinNums.xO (BinNums.xO BinNums.xH)))
                              (EnvRing.PEadd
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH)))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH))))
                           (EnvRing.PEadd
                              (EnvRing.PEX (BinNums.xI 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.xH;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                     |} tt))) None
            (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.PEadd
                                 (EnvRing.PEadd
                                    (EnvRing.PEX
                                       (BinNums.xO (BinNums.xO BinNums.xH)))
                                    (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH))))
                              (EnvRing.PEadd
                                 (EnvRing.PEX (BinNums.xI BinNums.xH))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                        |} tt)
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEX (BinNums.xO BinNums.xH);
                          RingMicromega.Fop := RingMicromega.OpEq;
                          RingMicromega.Frhs :=
                            EnvRing.PEsub
                              (EnvRing.PEadd
                                 (EnvRing.PEadd
                                    (EnvRing.PEX
                                       (BinNums.xO (BinNums.xO BinNums.xH)))
                                    (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH))))
                              (EnvRing.PEadd
                                 (EnvRing.PEX (BinNums.xI BinNums.xH))
                                 (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                        |} tt))
                  (Tauto.AND
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEsub
                              (EnvRing.PEadd
                                 (EnvRing.PEadd
                                    (EnvRing.PEX
                                       (BinNums.xO (BinNums.xO BinNums.xH)))
                                    (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                                 (EnvRing.PEX
                                    (BinNums.xI (BinNums.xO BinNums.xH))))
                              (EnvRing.PEadd
                                 (EnvRing.PEX (BinNums.xI 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.A Tauto.isProp
                  {|
                    RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                    RingMicromega.Fop := RingMicromega.OpEq;
                    RingMicromega.Frhs := EnvRing.PEX (BinNums.xO BinNums.xH)
                  |} tt))
       : Tauto.BFormula (RingMicromega.Formula BinNums.Z) Tauto.isProp
  ============================
   (BinInt.Z.lt BinNums.Z0
      (BinInt.Z.sub
         (BinInt.Z.add __x4 (BinInt.Z.add __x5 (BinNums.Zpos BinNums.xH)))
         (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH)))
    ∧ __x1 =
      BinInt.Z.sub
        (BinInt.Z.add __x4 (BinInt.Z.add __x5 (BinNums.Zpos BinNums.xH)))
        (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
    ∨ BinInt.Z.le
        (BinInt.Z.sub
           (BinInt.Z.add __x4 (BinInt.Z.add __x5 (BinNums.Zpos BinNums.xH)))
           (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))) BinNums.Z0
      ∧ __x1 = BinNums.Z0
    → BinInt.Z.lt BinNums.Z0
        (BinInt.Z.sub
           (BinInt.Z.add (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH)) __x5)
           (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH)))
      ∧ __x2 =
        BinInt.Z.sub
          (BinInt.Z.add (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH)) __x5)
          (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
      ∨ BinInt.Z.le
          (BinInt.Z.sub
             (BinInt.Z.add (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH)) __x5)
             (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))) BinNums.Z0
        ∧ __x2 = BinNums.Z0 → __x1 = __x2)


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