Definition no_msg_from_imp from to d :
no_msg_from from d -> no_msg_from_to from to d.

Lemma no_msg_from_toE' from to s tms from' to':
valid s ->
no_msg_from_to from to s -> from' == from = false ->
no_msg_from_to from to (post_msg s (Msg tms from' to' true)).1.