Section ordre.
Variable A : Set.
Variable f g : A -> nat.
Definition e_lexfg (a b : A) := f a > f b \/ f a = f b /\ g a > g b.
End ordre.
Notation lexfg := (e_lexfg _) (only parsing).
(* <Warning> : Syntax is discontinued *)
Hint Resolve lexfg_systemSL.
Hint Resolve lexfg_app_l.
Hint Resolve lexfg_app_r.
Hint Resolve lexfg_lambda.
Hint Resolve lexfg_env_t.
Hint Resolve lexfg_env_s.
Hint Resolve lexfg_cons_t.

Theorem lexfg_cons_s :
forall (a : terms) (s s' : sub_explicits),
e_lexfg _ (e_P1 ws) (e_P2 ws) s s' ->
e_lexfg _ (e_P1 ws) (e_P2 ws) (cons a s) (cons a s').