(* to make the proof faster, we avoid unfolding of those definitions *)
Definition Jspec'_juicy_mem_equiv_def CS ext_link :=
  ext_spec_stable juicy_mem_equiv (JE_spec _ ( @OK_spec (Concurrent_Espec unit CS ext_link))).Definition Jspec'_hered_def CS ext_link :=
   ext_spec_stable age (JE_spec _ ( @OK_spec (Concurrent_Espec unit CS ext_link))).

Lemma lock_coherence_age_to ge n m (tp : jstate ge) Phi : lock_coherence (lset tp) Phi m -> lock_coherence (AMap.map (option_map (age_to n)) (lset tp)) (age_to n Phi) m.