Goal:
  
  __p3 : Prop
  __p2 : Prop
  __p1 : Prop
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  __wit := (ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                    (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof
            :: 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 3)
                          (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 3)
                          (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 3))
                             (RingMicromega.PsatzIn Z 0)))
                       ZMicromega.DoneProof :: nil)%list
        : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
                (VarMap.Elt __x3) : VarMap.t Z
  __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.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.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.X Tauto.isProp __p2)
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs := EnvRing.PEX 4;
                          RingMicromega.Fop := RingMicromega.OpEq;
                          RingMicromega.Frhs :=
                            EnvRing.PEsub (EnvRing.PEX 3) (EnvRing.PEX 2)
                        |} tt))
                  (Tauto.AND
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs :=
                            EnvRing.PEsub (EnvRing.PEX 3) (EnvRing.PEX 2);
                          RingMicromega.Fop := RingMicromega.OpLe;
                          RingMicromega.Frhs := EnvRing.PEc 0%Z
                        |} tt) (Tauto.X Tauto.isProp __p3))) None
               (Tauto.IMPL
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEc 0%Z;
                       RingMicromega.Fop := RingMicromega.OpLe;
                       RingMicromega.Frhs := EnvRing.PEX 2
                     |} tt) None
                  (Tauto.IMPL
                     (Tauto.NOT
                        (Tauto.A Tauto.isProp
                           {|
                             RingMicromega.Flhs := EnvRing.PEX 3;
                             RingMicromega.Fop := RingMicromega.OpLe;
                             RingMicromega.Frhs := EnvRing.PEX 2
                           |} tt)) None
                     (Tauto.A Tauto.isProp
                        {|
                          RingMicromega.Flhs := EnvRing.PEX 1;
                          RingMicromega.Fop := RingMicromega.OpEq;
                          RingMicromega.Frhs := EnvRing.PEX 2
                        |} tt))))
       : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (__p1 /\ __x1 = (__x3 - __x4)%Z \/ (__x3 - __x4 <= 0)%Z /\ __x1 = 0%Z ->
    __p2 /\ __x4 = (__x3 - __x2)%Z \/ (__x3 - __x2 <= 0)%Z /\ __p3 ->
    (0 <= __x2)%Z -> ((__x3 <= __x2)%Z -> False) -> __x1 = __x2)


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