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 p p' p'' lp1 lp2 :
FA_path p p' lp1 /\ FA_path p' p'' lp2 -> FA_path p p'' (lp1 ++ lp2).