Goal:
    __x4 : Z  __x3 : Z  __x2 : Z  __x1 : Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
               (RingMicromega.PsatzAdd (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.A Tauto.isProp
           {|
             RingMicromega.Flhs := EnvRing.PEc 0;
             RingMicromega.Fop := RingMicromega.OpLe;
             RingMicromega.Frhs := EnvRing.PEX 3
           |} tt) None
        (Tauto.IMPL
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs :=
                  EnvRing.PEadd (EnvRing.PEX 1) (EnvRing.PEX 4);
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs := EnvRing.PEc 0
              |} tt) None
           (Tauto.IMPL
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX 2;
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEX 4
                 |} tt) None
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs :=
                     EnvRing.PEadd (EnvRing.PEX 1) (EnvRing.PEX 2);
                   RingMicromega.Fop := RingMicromega.OpLe;
                   RingMicromega.Frhs := EnvRing.PEX 3
                 |} tt))) in
    0 <= __x3 -> __x1 + __x4 <= 0 -> __x2 <= __x4 -> __x1 + __x2 <= __x3)


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))