Hint Resolve type_move_incr: ty.

(* Specifications: *)
Lemma type_move_sound:
forall te e r1 r2 e' changed,
type_move e r1 r2 = OK(changed, e') -> satisf te e' -> T.sub (te r1) (te r2).
Lemma solve_rec_incr:
forall te q e changed e' changed',
solve_rec e changed q = OK(e', changed') -> satisf te e' -> satisf te e.
Lemma solve_rec_sound:
forall te r1 r2 q e changed e' changed',
solve_rec e changed q = OK(e', changed') -> In (r1, r2) q -> satisf te e' ->
T.sub (te r1) (te r2).
Lemma type_move_false:
forall e r1 r2 e',
type_move e r1 r2 = OK(false, e') ->
te_typ e' = te_typ e /\ T.sub (makeassign e r1) (makeassign e r2).
Lemma solve_rec_false:
forall r1 r2 q e changed e',
solve_rec e changed q = OK(e', false) ->
changed = false /\
(In (r1, r2) q -> T.sub (makeassign e r1) (makeassign e r2)).
Lemma solve_constraints_incr:
forall te e e', solve_constraints e = OK e' -> satisf te e' -> satisf te e.
Lemma solve_constraints_sound:
forall e e', solve_constraints e = OK e' -> satisf (makeassign e') e'.
Theorem solve_sound:
forall e te, solve e = OK te -> satisf te e.
Lemma type_move_sound:
forall te e r1 r2 e' changed,
type_move e r1 r2 = OK(changed, e') -> satisf te e' -> T.sub (te r1) (te r2).
Lemma solve_rec_incr:
forall te q e changed e' changed',
solve_rec e changed q = OK(e', changed') -> satisf te e' -> satisf te e.
Lemma solve_rec_sound:
forall te r1 r2 q e changed e' changed',
solve_rec e changed q = OK(e', changed') -> In (r1, r2) q -> satisf te e' ->
T.sub (te r1) (te r2).
Lemma type_move_false:
forall e r1 r2 e',
type_move e r1 r2 = OK(false, e') ->
te_typ e' = te_typ e /\ T.sub (makeassign e r1) (makeassign e r2).
Lemma solve_rec_false:
forall r1 r2 q e changed e',
solve_rec e changed q = OK(e', false) ->
changed = false /\
(In (r1, r2) q -> T.sub (makeassign e r1) (makeassign e r2)).
Lemma solve_constraints_incr:
forall te e e', solve_constraints e = OK e' -> satisf te e' -> satisf te e.
Lemma solve_constraints_sound:
forall e e', solve_constraints e = OK e' -> satisf (makeassign e') e'.
Theorem solve_sound:
forall e te, solve e = OK te -> satisf te e.