Fixpoint FA_path p p' (lp : list cbv) := match lp with
| [] => p = p'
| h :: t => In p (first_activations h) /\ FA_path h p' t
end.

Lemma FA_path_app_destruct p p' lp1 lp2 : FA_path p p' (lp1 ++ lp2) ->
exists p'', FA_path p p'' lp1 /\ FA_path p'' p' lp2.