Goal:
    __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 4))
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 1)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 1)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 2)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd
            (RingMicromega.PsatzMulC (EnvRing.Pc (BinNums.Zneg BinNums.xH))
               (RingMicromega.PsatzIn BinNums.Z 4))
            (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.PsatzIn BinNums.Z 4)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof] in
    let __varmap := VarMap.Branch (VarMap.Elt __x2) __x1 (VarMap.Elt __x3) 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.PEX (BinNums.xI BinNums.xH))
                       (EnvRing.PEc BinNums.Z0)
                 |} tt)
              (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.PEc BinNums.Z0)
                 |} tt))
           (Tauto.AND
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEsub (EnvRing.PEX (BinNums.xI BinNums.xH))
                       (EnvRing.PEc BinNums.Z0);
                   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.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.xH)
                             (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                          (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                    |} tt)
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs :=
                        EnvRing.PEX (BinNums.xI BinNums.xH);
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs :=
                        EnvRing.PEsub
                          (EnvRing.PEadd (EnvRing.PEX BinNums.xH)
                             (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                          (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                    |} tt))
              (Tauto.AND
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs :=
                        EnvRing.PEsub
                          (EnvRing.PEadd (EnvRing.PEX BinNums.xH)
                             (EnvRing.PEc (BinNums.Zpos 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.xI 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.xH
                 |} 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 __x3 BinNums.Z0)
    ∧ __x2 = BinInt.Z.sub __x3 BinNums.Z0
    ∨ BinInt.Z.le (BinInt.Z.sub __x3 BinNums.Z0) BinNums.Z0
      ∧ __x2 = BinNums.Z0
    → BinInt.Z.lt BinNums.Z0
        (BinInt.Z.sub (BinInt.Z.add __x1 (BinNums.Zpos BinNums.xH))
           (BinNums.Zpos BinNums.xH))
      ∧ __x3 =
        BinInt.Z.sub (BinInt.Z.add __x1 (BinNums.Zpos BinNums.xH))
          (BinNums.Zpos BinNums.xH)
      ∨ BinInt.Z.le
          (BinInt.Z.sub (BinInt.Z.add __x1 (BinNums.Zpos BinNums.xH))
             (BinNums.Zpos BinNums.xH)) BinNums.Z0 ∧ 
        __x3 = BinNums.Z0 → BinInt.Z.le BinNums.Z0 __x1 → __x1 = __x2)


DEBUG:Going to execute:
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))