Goal:
  
  __p2 : Prop
  __p1 : Prop
  __x5 : Z
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
               (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
               (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof] in
    let __varmap :=
      VarMap.Branch (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
        (VarMap.Branch VarMap.Empty __x3 (VarMap.Elt __x5)) in
    let __ff :=
      Tauto.IMPL
        (Tauto.OR
           (Tauto.AND (Tauto.X Tauto.isProp __p1)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 2;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs :=
                     EnvRing.PEsub
                       (EnvRing.PEsub (EnvRing.PEX 4) (EnvRing.PEX 3))
                       (EnvRing.PEX 7)
                 |} tt))
           (Tauto.AND (Tauto.X Tauto.isProp __p2)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 2;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEc 0
                 |} tt))) None
        (Tauto.IMPL
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs := EnvRing.PEX 1;
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs := EnvRing.PEX 7
              |} tt) None
           (Tauto.IMPL
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEadd (EnvRing.PEX 3) (EnvRing.PEX 1);
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEX 4
                 |} tt) None
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEadd (EnvRing.PEX 1)
                       (EnvRing.PEadd (EnvRing.PEX 2) (EnvRing.PEX 3));
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEX 4
                 |} tt))) in
    __p1 /\ __x2 = __x4 - __x3 - __x5 \/ __p2 /\ __x2 = 0 ->
    __x1 <= __x5 -> __x3 + __x1 <= __x4 -> __x1 + (__x2 + __x3) <= __x4)


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