Section InvMachineLemmas.
intros js age a R. simpl; unfold OrdinalPool.lockRes; destruct js.
simpl.
intros AA.
apply AMap_find_map_inv in AA. destruct AA as [[? x] [map rest]].
inv rest.
rewrite map. f_equal; f_equal.
destruct x; inversion H1; reflexivity.
Qed.

Lemma mem_cohere_age_to n m phi :
mem_cohere' m phi ->
mem_cohere' m (age_to n phi).