Section JuicyMachineLemmas.
intros js age a. simpl; unfold OrdinalPool.lockRes; destruct js.
simpl.
intros AA.
apply AMap_find_map_inv in AA. destruct AA as [x [map rest]].
rewrite map. f_equal.
destruct x; inversion rest; try reflexivity.
Qed.

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