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


DEBUG:Going to execute:
<coq-core.plugins.ltac::exact@0> $1