Goal:
  
  __p2 : Prop
  __p1 : Prop
  __x5 : Z
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  __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]
        : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch
                (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
                (VarMap.Branch VarMap.Empty __x3 (VarMap.Elt __x5))
           : VarMap.t Z
  __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)))
       : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (__p1 /\ __x2 = __x4 - __x3 - __x5 \/ __p2 /\ __x2 = 0 ->
    __x1 <= __x5 -> __x3 + __x1 <= __x4 -> __x1 + (__x2 + __x3) <= __x4)


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