Goal:
    __x3 : BinNums.Z  __x2 : BinNums.Z  __x1 : BinNums.Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 1)
               (RingMicromega.PsatzIn BinNums.Z 0))) ZMicromega.DoneProof] in
    let __varmap := VarMap.Branch (VarMap.Elt __x2) __x1 (VarMap.Elt __x3) in
    let __ff :=
      Tauto.IMPL
        (Tauto.A Tauto.isProp
           {|
             RingMicromega.Flhs := EnvRing.PEc BinNums.Z0;
             RingMicromega.Fop := RingMicromega.OpLe;
             RingMicromega.Frhs := EnvRing.PEX (BinNums.xI BinNums.xH)
           |} tt) None
        (Tauto.IMPL
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs := EnvRing.PEX (BinNums.xO BinNums.xH)
              |} tt) None
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                RingMicromega.Fop := RingMicromega.OpLt;
                RingMicromega.Frhs :=
                  EnvRing.PEadd (EnvRing.PEX (BinNums.xO BinNums.xH))
                    (EnvRing.PEadd (EnvRing.PEX (BinNums.xI BinNums.xH))
                       (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
              |} tt)) in
    BinInt.Z.le BinNums.Z0 __x3
    → BinInt.Z.le __x1 __x2
      → BinInt.Z.lt __x1
          (BinInt.Z.add __x2 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))))


DEBUG:Going to execute:
zchecker