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.