Goal:
  
  __x5 : Z
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  __wit := [ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 1)
                    (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof]
        : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
                (VarMap.Branch (VarMap.Elt __x5) __x3 VarMap.Empty)
           : VarMap.t Z
  __ff := Tauto.IMPL
            (Tauto.A Tauto.isProp
               {|
                 RingMicromega.Flhs :=
                   EnvRing.PEadd (EnvRing.PEX 5) (EnvRing.PEX 3);
                 RingMicromega.Fop := RingMicromega.OpLe;
                 RingMicromega.Frhs := EnvRing.PEX 4
               |} tt) None
            (Tauto.IMPL
               (Tauto.A Tauto.isProp
                  {|
                    RingMicromega.Flhs :=
                      EnvRing.PEadd (EnvRing.PEX 1) (EnvRing.PEX 2);
                    RingMicromega.Fop := RingMicromega.OpLe;
                    RingMicromega.Frhs := EnvRing.PEX 5
                  |} 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))
       : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (__x5 + __x3 <= __x4 ->
    __x1 + __x2 <= __x5 -> __x1 + (__x2 + __x3) <= __x4)


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