Definition cbv_cache_entry (proof_tree : cbv) := (proj_left proof_tree, proj_right proof_tree).

Lemma cache_content_on_path c1 c2 lp:
andl (map wf lp) ->
cache_path c1 c2 lp = true ->
c2 = map cbv_cache_entry (revflatten (map activations_cache_order lp)) ++ c1.