Goal:
  
  __x4 : Z
  __x3 : Z
  __x2 : Z
  __x1 : Z
  __wit := [ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (RingMicromega.PsatzIn Z 2))
                    (RingMicromega.PsatzIn Z 1))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (RingMicromega.PsatzIn Z 2))
                    (RingMicromega.PsatzIn Z 1))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (RingMicromega.PsatzIn Z 3))
                    (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                       (RingMicromega.PsatzIn Z 0)))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd
                 (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                    (RingMicromega.PsatzIn Z 3))
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                    (RingMicromega.PsatzIn Z 1))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (RingMicromega.PsatzIn Z 3))
                    (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                       (RingMicromega.PsatzIn Z 1)))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 4)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (RingMicromega.PsatzIn Z 3))
                    (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                       (RingMicromega.PsatzIn Z 1)))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd
                 (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                    (RingMicromega.PsatzIn Z 3))
                 (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 2)
                    (RingMicromega.PsatzIn Z 0))) ZMicromega.DoneProof;
            ZMicromega.RatProof
              (RingMicromega.PsatzAdd (RingMicromega.PsatzIn Z 3)
                 (RingMicromega.PsatzAdd
                    (RingMicromega.PsatzMulC (EnvRing.Pc (-1))
                       (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.OR
               (Tauto.AND
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 1;
                       RingMicromega.Fop := RingMicromega.OpLt;
                       RingMicromega.Frhs := EnvRing.PEX 3
                     |} tt)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 4;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEX 3
                     |} tt))
               (Tauto.AND
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 3;
                       RingMicromega.Fop := RingMicromega.OpLe;
                       RingMicromega.Frhs := EnvRing.PEX 1
                     |} tt)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 4;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEX 1
                     |} tt))) None
            (Tauto.IMPL
               (Tauto.A Tauto.isProp
                  {|
                    RingMicromega.Flhs := EnvRing.PEX 4;
                    RingMicromega.Fop := RingMicromega.OpEq;
                    RingMicromega.Frhs := EnvRing.PEX 2
                  |} tt) None
               (Tauto.OR
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 1;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEX 2
                     |} tt)
                  (Tauto.A Tauto.isProp
                     {|
                       RingMicromega.Flhs := EnvRing.PEX 3;
                       RingMicromega.Fop := RingMicromega.OpEq;
                       RingMicromega.Frhs := EnvRing.PEX 2
                     |} tt)))
       : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (__x1 < __x3 /\ __x4 = __x3 \/ __x3 <= __x1 /\ __x4 = __x1 ->
    __x4 = __x2 -> __x1 = __x2 \/ __x3 = __x2)


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