Goal:
  
  __x2 : Z
  __x1 : Z
  __wit := nil : list ZMicromega.ZArithProof
  __varmap := VarMap.Branch (VarMap.Elt __x2) __x1 VarMap.Empty : VarMap.t Z
  __ff := Tauto.IMPL
            (Tauto.NOT
               (Tauto.A Tauto.isProp
                  {|
                    RingMicromega.Flhs := EnvRing.PEX 2;
                    RingMicromega.Fop := RingMicromega.OpLe;
                    RingMicromega.Frhs := EnvRing.PEX 1
                  |} tt)) None
            (Tauto.A Tauto.isProp
               {|
                 RingMicromega.Flhs := EnvRing.PEX 1;
                 RingMicromega.Fop := RingMicromega.OpLt;
                 RingMicromega.Frhs := EnvRing.PEX 2
               |} tt) : Tauto.BFormula (RingMicromega.Formula Z) Tauto.isProp
  ============================
   (((__x2 <= __x1)%Z -> False) -> (__x1 < __x2)%Z)


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

Goals:

DEBUG:Going to execute:
easy

Goals:

DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ /\ _ => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:

DEBUG:Going to execute:
let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:

DEBUG:Going to execute:
let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:

DEBUG:Going to execute:
solve
[ trivial with eq_true | reflexivity | symmetry; trivial | contradiction ]

Goals:

DEBUG:Going to execute:
let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:

DEBUG:Going to execute:
(solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

File "./theories/MCArith.v", line 19, characters 2-15:
Warning: There is no flag or option with this name: "Debug On".
[unknown-option,default]
File "./theories/MCArith.v", line 17, characters 2-16:
Warning: There is no flag or option with this name: "Debug Off".
[unknown-option,default]
File "./theories/MCArith.v", line 19, characters 2-15:
Warning: There is no flag or option with this name: "Debug On".
[unknown-option,default]