(* this suggest capturing the pattern by means of a new definition *)
Definition after A s (p : proc A) (P : A -> state -> Prop) :=
always s p (fun s2 p2 => forall v, p2 = Ret v -> P v s2).

Lemma aftI A s (p : proc A) (P : Prop) (Q : A -> state -> Prop) :
alwsafe s p ->
after s p (fun v s' => P -> Q v s') <->
(P -> after s p (fun v s' => Q v s')).