Notation getl := (getLocal).Notation gets := getStatelet.Notation getp := (@getProtocol _ w).Definition network_rely s1 s2 := exists n, network_rely' n s1 s2.

Lemma rely_consume_other l s s' m tm from: network_rely s s' -> find m (dsoup (gets s l)) = Some (Msg tm from this true) -> find m (dsoup (gets s' l)) = Some (Msg tm from this true).