Goal:
  
  s : t
  s' : t
  e : match compare s s' with
      | Eq => true
      | _ => false
      end = true
  ============================
   (s = s')


DEBUG:Going to execute:
t

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


DEBUG:Going to execute:
easy
DEBUG LTAC Evaluated term: (compare_spec s s')

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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
           | Ltac.reflexivity
           | Ltac.symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ Ltac.split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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
           | Ltac.reflexivity
           | Ltac.symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ Ltac.split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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

Goals:
    s : t  s' : t  e : true = true  H : s = s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s s'
  ============================
   (s = s')

    s : t  s' : t  e : false = true  H : lt s' s
  ============================
   (s = s')


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