Goal:
  
  __p3 : Prop
  __p2 : Prop
  __p1 : Prop
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  ============================
   (let __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 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.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)))) in
    __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:
intros __wit __varmap __ff; exact
            (ZMicromega.ZTautoChecker_sound __ff __wit
               (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
               (VarMap.find 0%Z __varmap))