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

(* Specifications: *)
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.
Lemma msg_specE s from to tg cnt :
valid s ->
no_msg_from_to from to s ->
msg_spec from to tg cnt (post_msg s (Msg (TMsg tg cnt) from to true)).1.
Lemma msg_specE' s from to to' tg cnt tms :
valid s -> to == to' = false ->
msg_spec from to tg cnt s ->
msg_spec from to tg cnt (post_msg s (Msg tms from to' true)).1.
Lemma msg_specE'' s from from' to to' tg cnt tms :
valid s -> from == from' = false ->
msg_spec from to tg cnt s ->
msg_spec from to tg cnt (post_msg s (Msg tms from' to' true)).1.