Goal:
  
  __x6 : BinNums.Z
  __x5 : BinNums.Z
  __x4 : BinNums.Z
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  __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] : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 (VarMap.Elt __x6)) __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.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)))))
       : Tauto.BFormula (RingMicromega.Formula BinNums.Z) Tauto.isProp
  ============================
   (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:
exact
(ZMicromega.ZTautoChecker_sound __ff __wit
   (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
   (VarMap.find BinNums.Z0 __varmap))