(** Lemmas common to both parts of the progress/preservation simulation results *)

(* Most general lemma about preservation of matchfunspecs *)
Lemma pures_eq_matchfunspecs e Gamma Phi Phi' :
(level Phi' <= level Phi)%nat ->
pures_eq Phi Phi' ->
matchfunspecs e Gamma Phi ->
matchfunspecs e Gamma Phi'.