Goal:
    __x4 : BinNums.Z  __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.Branch (VarMap.Elt __x4) __x2 VarMap.Empty) __x1
        (VarMap.Elt __x3) in
    let __ff :=
      Tauto.IMPL
        (Tauto.A Tauto.isProp
           {|
             RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
             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.xO BinNums.xH);
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs :=
                  EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH))
              |} tt) None
           (Tauto.A Tauto.isProp
              {|
                RingMicromega.Flhs :=
                  EnvRing.PEadd
                    (EnvRing.PEadd (EnvRing.PEX BinNums.xH)
                       (EnvRing.PEX (BinNums.xO BinNums.xH)))
                    (EnvRing.PEc (BinNums.Zpos BinNums.xH));
                RingMicromega.Fop := RingMicromega.OpLe;
                RingMicromega.Frhs :=
                  EnvRing.PEadd
                    (EnvRing.PEadd (EnvRing.PEX (BinNums.xI BinNums.xH))
                       (EnvRing.PEX (BinNums.xO (BinNums.xO BinNums.xH))))
                    (EnvRing.PEc (BinNums.Zpos BinNums.xH))
              |} tt)) in
    BinInt.Z.le __x1 __x3
    → BinInt.Z.le __x2 __x4
      → BinInt.Z.le
          (BinInt.Z.add (BinInt.Z.add __x1 __x2) (BinNums.Zpos BinNums.xH))
          (BinInt.Z.add (BinInt.Z.add __x3 __x4) (BinNums.Zpos BinNums.xH)))


DEBUG:Going to execute:
zchecker