Goal:
  
  __x6 : BinNums.Z
  __x5 : BinNums.Z
  __x4 : BinNums.Z
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 4))
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd
            (RingMicromega.PsatzMulC (EnvRing.Pc (BinNums.Zneg BinNums.xH))
               (RingMicromega.PsatzIn BinNums.Z 8))
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd
            (RingMicromega.PsatzMulC (EnvRing.Pc (BinNums.Zneg BinNums.xH))
               (RingMicromega.PsatzIn BinNums.Z 8))
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 4))
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 7)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                  (RingMicromega.PsatzIn BinNums.Z 1)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 7)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                  (RingMicromega.PsatzIn BinNums.Z 1)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (RingMicromega.PsatzIn BinNums.Z 1))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd
                  (RingMicromega.PsatzMulC
                     (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                     (RingMicromega.PsatzIn BinNums.Z 4))
                  (RingMicromega.PsatzIn BinNums.Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 6))
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
                  (RingMicromega.PsatzIn BinNums.Z 2)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd
                  (RingMicromega.PsatzMulC
                     (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                     (RingMicromega.PsatzIn BinNums.Z 4))
                  (RingMicromega.PsatzIn BinNums.Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 4))
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd
            (RingMicromega.PsatzMulC (EnvRing.Pc (BinNums.Zneg BinNums.xH))
               (RingMicromega.PsatzIn BinNums.Z 8))
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 6)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
                  (RingMicromega.PsatzMulC
                     (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                     (RingMicromega.PsatzIn BinNums.Z 2)))))
         ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 6)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
                  (RingMicromega.PsatzMulC
                     (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                     (RingMicromega.PsatzIn BinNums.Z 2)))))
         ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 8)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 6)
               (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.PsatzMulC (EnvRing.Pc (BinNums.Zneg BinNums.xH))
               (RingMicromega.PsatzIn BinNums.Z 8))
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 6))
               (RingMicromega.PsatzAdd (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 5)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (RingMicromega.PsatzIn BinNums.Z 1))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (RingMicromega.PsatzIn BinNums.Z 1))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 7)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                  (RingMicromega.PsatzIn BinNums.Z 1)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 7)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 5)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
                  (RingMicromega.PsatzIn BinNums.Z 1)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 6)
               (RingMicromega.PsatzIn BinNums.Z 1))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 8))
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
                  (RingMicromega.PsatzIn BinNums.Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC
                  (EnvRing.Pc (BinNums.Zneg BinNums.xH))
                  (RingMicromega.PsatzIn BinNums.Z 8))
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 4)
                  (RingMicromega.PsatzIn BinNums.Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 9)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 6)
               (RingMicromega.PsatzIn BinNums.Z 1))) ZMicromega.DoneProof] in
    let __varmap :=
      VarMap.Branch (VarMap.Branch (VarMap.Elt __x4) __x2 (VarMap.Elt __x6))
        __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.PEX (BinNums.xO (BinNums.xI 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.PEX (BinNums.xO (BinNums.xI BinNums.xH)))
                       (EnvRing.PEX (BinNums.xI BinNums.xH))
                 |} tt))
           (Tauto.AND
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEsub
                       (EnvRing.PEX (BinNums.xO (BinNums.xI 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.PEX (BinNums.xO (BinNums.xO BinNums.xH)))
                          (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                    |} tt)
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs :=
                        EnvRing.PEX (BinNums.xO (BinNums.xI BinNums.xH));
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs :=
                        EnvRing.PEsub
                          (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.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.xI 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.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.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.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.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.PEc (BinNums.Zpos BinNums.xH)))
                                (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                          |} tt)
                       (Tauto.A Tauto.isProp
                          {|
                            RingMicromega.Flhs :=
                              EnvRing.PEX
                                (BinNums.xI (BinNums.xO BinNums.xH));
                            RingMicromega.Fop := RingMicromega.OpEq;
                            RingMicromega.Frhs :=
                              EnvRing.PEsub
                                (EnvRing.PEadd
                                   (EnvRing.PEX
                                      (BinNums.xO (BinNums.xO 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.xO (BinNums.xO 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.xO 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.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 __x6 __x3)
    ∧ __x1 = BinInt.Z.sub __x6 __x3
    ∨ BinInt.Z.le (BinInt.Z.sub __x6 __x3) BinNums.Z0 ∧ __x1 = BinNums.Z0
    → BinInt.Z.lt BinNums.Z0 (BinInt.Z.sub __x4 (BinNums.Zpos BinNums.xH))
      ∧ __x6 = BinInt.Z.sub __x4 (BinNums.Zpos BinNums.xH)
      ∨ BinInt.Z.le (BinInt.Z.sub __x4 (BinNums.Zpos BinNums.xH)) BinNums.Z0
        ∧ __x6 = BinNums.Z0
      → BinInt.Z.lt BinNums.Z0
          (BinInt.Z.sub __x5 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH)))
        ∧ __x2 =
          BinInt.Z.sub __x5 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
        ∨ BinInt.Z.le
            (BinInt.Z.sub __x5 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH)))
            BinNums.Z0 ∧ __x2 = BinNums.Z0
        → BinInt.Z.lt BinNums.Z0
            (BinInt.Z.sub (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH))
               (BinNums.Zpos BinNums.xH))
          ∧ __x5 =
            BinInt.Z.sub (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH))
              (BinNums.Zpos BinNums.xH)
          ∨ BinInt.Z.le
              (BinInt.Z.sub (BinInt.Z.add __x4 (BinNums.Zpos BinNums.xH))
                 (BinNums.Zpos BinNums.xH)) BinNums.Z0 ∧ 
            __x5 = BinNums.Z0 → BinInt.Z.le BinNums.Z0 __x3 → __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))