Goal:
    __p1 : Prop  __x4 : Z  __x3 : Z  __x2 : Z  __x1 : Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
            (RingMicromega.PsatzAdd
               (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                  (RingMicromega.PsatzIn Z 1)) (RingMicromega.PsatzIn Z 0)))
         ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd
            (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
               (RingMicromega.PsatzIn Z 1)) (RingMicromega.PsatzIn Z 0))
         ZMicromega.DoneProof] 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 3;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs :=
                     EnvRing.PEsub
                       (EnvRing.PEsub (EnvRing.PEX 1) (EnvRing.PEX 2))
                       (EnvRing.PEX 4)
                 |} tt))
           (Tauto.AND
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEsub
                       (EnvRing.PEsub (EnvRing.PEX 1) (EnvRing.PEX 2))
                       (EnvRing.PEX 4);
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEc 0
                 |} tt)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 3;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEc 0
                 |} tt))) None
        (Tauto.A Tauto.isProp
           {|
             RingMicromega.Flhs :=
               EnvRing.PEsub (EnvRing.PEX 1)
                 (EnvRing.PEadd (EnvRing.PEX 2) (EnvRing.PEX 3));
             RingMicromega.Fop := RingMicromega.OpLe;
             RingMicromega.Frhs := EnvRing.PEX 4
           |} tt) in
    __p1 /\ __x3 = __x1 - __x2 - __x4 \/ __x1 - __x2 - __x4 <= 0 /\ __x3 = 0 ->
    __x1 - (__x2 + __x3) <= __x4)


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