Goal:
  
  __x5 : BinNums.Z
  __x4 : BinNums.Z
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  ============================
   (let __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] in
    let __varmap :=
      VarMap.Branch (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
        (VarMap.Branch (VarMap.Elt __x5) __x3 VarMap.Empty) in
    let __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.PEX (BinNums.xI (BinNums.xO BinNums.xH))))
                       (EnvRing.PEX (BinNums.xI 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.PEX (BinNums.xI (BinNums.xO BinNums.xH))))
                       (EnvRing.PEX (BinNums.xI BinNums.xH))
                 |} tt))
           (Tauto.AND
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEsub
                       (EnvRing.PEadd
                          (EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH)))
                          (EnvRing.PEX (BinNums.xI (BinNums.xO BinNums.xH))))
                       (EnvRing.PEX (BinNums.xI 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.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.xO 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.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)) in
    BinInt.Z.lt BinNums.Z0 (BinInt.Z.sub (BinInt.Z.add __x4 __x5) __x3)
    ∧ __x1 = BinInt.Z.sub (BinInt.Z.add __x4 __x5) __x3
    ∨ BinInt.Z.le (BinInt.Z.sub (BinInt.Z.add __x4 __x5) __x3) BinNums.Z0
      ∧ __x1 = BinNums.Z0
    → 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)))
      ∧ __x2 =
        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
        ∧ __x2 = BinNums.Z0 → __x1 = __x2)


DEBUG:Going to execute:
let __wit := fresh "__wit" in
           let __varmap := fresh "__varmap" in
           let __ff := fresh "__ff" in
           intros __wit __varmap __ff; exact
            (ZMicromega.ZTautoChecker_sound __ff __wit
               (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
               (VarMap.find BinNums.Z0 __varmap))