Goal:
    __p2 : Prop  __p1 : Prop  __x4 : Z  __x3 : Z  __x2 : Z  __x1 : Z
  ============================
   (let __wit :=
      (ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 5)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC (EnvRing.Pc (-1)%Z)
                  (RingMicromega.PsatzIn Z 4))
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                  (RingMicromega.PsatzIn Z 0)))) ZMicromega.DoneProof
       :: ZMicromega.RatProof
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
                  (RingMicromega.PsatzAdd
                     (RingMicromega.PsatzMulC (EnvRing.Pc (-1)%Z)
                        (RingMicromega.PsatzIn Z 2))
                     (RingMicromega.PsatzIn Z 0)))) ZMicromega.DoneProof
          :: ZMicromega.RatProof
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
                  (RingMicromega.PsatzAdd
                     (RingMicromega.PsatzMulC (EnvRing.Pc (-1)%Z)
                        (RingMicromega.PsatzIn Z 2))
                     (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof
             :: ZMicromega.RatProof
                  (RingMicromega.PsatzAdd
                     (RingMicromega.PsatzMulC (EnvRing.Pc (-1)%Z)
                        (RingMicromega.PsatzIn Z 4))
                     (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                        (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof
                :: nil)%list in
    let __varmap :=
      VarMap.Branch (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
        (VarMap.Elt __x3) in
    let __ff :=
      Tauto.IMPL
        (Tauto.OR
           (Tauto.AND (Tauto.X Tauto.isProp __p1)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 1;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs :=
                     EnvRing.PEsub (EnvRing.PEX 3)
                       (EnvRing.PEadd (EnvRing.PEX 4) (EnvRing.PEc 1%Z))
                 |} tt))
           (Tauto.AND
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEsub (EnvRing.PEX 3)
                       (EnvRing.PEadd (EnvRing.PEX 4) (EnvRing.PEc 1%Z));
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEc 0%Z
                 |} tt)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 1;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEc 0%Z
                 |} tt))) None
        (Tauto.IMPL
           (Tauto.OR
              (Tauto.AND
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEc 0%Z;
                      RingMicromega.Fop := RingMicromega.OpLt;
                      RingMicromega.Frhs :=
                        EnvRing.PEsub (EnvRing.PEX 3) (EnvRing.PEX 4)
                    |} tt)
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 2;
                      RingMicromega.Fop := RingMicromega.OpEq;
                      RingMicromega.Frhs :=
                        EnvRing.PEsub (EnvRing.PEX 3) (EnvRing.PEX 4)
                    |} tt))
              (Tauto.AND
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs :=
                        EnvRing.PEsub (EnvRing.PEX 3) (EnvRing.PEX 4);
                      RingMicromega.Fop := RingMicromega.OpLe;
                      RingMicromega.Frhs := EnvRing.PEc 0%Z
                    |} tt) (Tauto.X Tauto.isProp __p2))) None
           (Tauto.IMPL
              (Tauto.NOT
                 (Tauto.A Tauto.isProp
                    {|
                      RingMicromega.Flhs := EnvRing.PEX 3;
                      RingMicromega.Fop := RingMicromega.OpLe;
                      RingMicromega.Frhs := EnvRing.PEX 4
                    |} tt)) None
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEadd (EnvRing.PEX 1) (EnvRing.PEc 1%Z);
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEX 2
                 |} tt))) in
    __p1 /\ __x1 = (__x3 - (__x4 + 1))%Z \/
    (__x3 - (__x4 + 1) <= 0)%Z /\ __x1 = 0%Z ->
    (0 < __x3 - __x4)%Z /\ __x2 = (__x3 - __x4)%Z \/
    (__x3 - __x4 <= 0)%Z /\ __p2 ->
    ((__x3 <= __x4)%Z -> False) -> (__x1 + 1)%Z = __x2)


DEBUG:Going to execute:
intros __wit __varmap __ff; exact
            (ZMicromega.ZTautoChecker_sound __ff __wit
               (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
               (VarMap.find 0%Z __varmap))