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


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