Goal:
  
  __p2 : Prop
  __p1 : Prop
  __x3 : BinNums.Z
  __x2 : BinNums.Z
  __x1 : BinNums.Z
  ============================
   (let __wit :=
      [ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 1)
                  (RingMicromega.PsatzIn BinNums.Z 0)))) ZMicromega.DoneProof;
       ZMicromega.RatProof
         (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 3)
            (RingMicromega.PsatzAdd (RingMicromega.PsatzIn BinNums.Z 2)
               (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.OR
           (Tauto.AND (Tauto.X Tauto.isProp __p1)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs :=
                     EnvRing.PEsub (EnvRing.PEX (BinNums.xO BinNums.xH))
                       (EnvRing.PEadd (EnvRing.PEX (BinNums.xI BinNums.xH))
                          (EnvRing.PEc (BinNums.Zpos BinNums.xH)))
                 |} tt))
           (Tauto.AND (Tauto.X Tauto.isProp __p2)
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                   RingMicromega.Fop := RingMicromega.OpEq;
                   RingMicromega.Frhs := EnvRing.PEc BinNums.Z0
                 |} tt))) None
        (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.PEadd (EnvRing.PEX (BinNums.xI BinNums.xH))
                       (EnvRing.PEc (BinNums.Zpos BinNums.xH));
                   RingMicromega.Fop := RingMicromega.OpLt;
                   RingMicromega.Frhs :=
                     EnvRing.PEadd (EnvRing.PEX (BinNums.xO BinNums.xH))
                       (EnvRing.PEc (BinNums.Zpos BinNums.xH))
                 |} tt) None
              (Tauto.A Tauto.isProp
                 {|
                   RingMicromega.Flhs := EnvRing.PEX BinNums.xH;
                   RingMicromega.Fop := RingMicromega.OpLt;
                   RingMicromega.Frhs := EnvRing.PEX (BinNums.xO BinNums.xH)
                 |} tt))) in
    __p1
    ∧ __x1 = BinInt.Z.sub __x2 (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
    ∨ __p2 ∧ __x1 = BinNums.Z0
    → BinInt.Z.le BinNums.Z0 __x3
      → BinInt.Z.lt (BinInt.Z.add __x3 (BinNums.Zpos BinNums.xH))
          (BinInt.Z.add __x2 (BinNums.Zpos BinNums.xH))
        → BinInt.Z.lt __x1 __x2)


DEBUG:Going to execute:
zchecker