Definition no_msg_from_imp from to d :
  no_msg_from from d -> no_msg_from_to from to d.(********************************************************)
(*** More elaborated versions of the same predicates  ***)
(********************************************************)

Definition no_msg_from_to' from to
           (criterion : nat -> seq nat -> bool) (d : soup) :=
  forall i t c,
    find i d = Some (Msg (TMsg t c) from to true) ->
    ~~criterion t c.

(* Specifications: *)
Lemma no_msg_from_to_consume' from to cond s i: valid s -> no_msg_from_to' from to cond s -> no_msg_from_to' from to cond (consume_msg s i).