Goal:
    __x4 : Z  __x3 : Z  __x2 : Z  __x1 : Z
  ============================
   (let __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] in
    let __varmap :=
      VarMap.Branch (VarMap.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
        (VarMap.Elt __x3) in
    let __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))) in
    __x1 < __x3 /\ __x4 = __x3 \/ __x3 <= __x1 /\ __x4 = __x1 ->
    __x4 = __x2 -> __x1 = __x2 \/ __x3 = __x2)


DEBUG:Going to execute:
let __wit := fresh "__wit" in
           let __varmap := fresh "__varmap" in
           let __ff := fresh "__ff" in
           intros __wit __varmap __ff; exact
            (ZMicromega.ZTautoChecker_sound __ff __wit
               (eq_refl <: ZMicromega.ZTautoChecker __ff __wit = true)
               (VarMap.find 0 __varmap))