Module fc_preservation (wf : fc_wf_sig) (weak : fc_weak_sig) (subst : fc_subst_sig)
(e_subst : ext_subst_sig).
Module e_invert := ext_invert e_subst.
Module red := ext_red e_invert.
Module red_one := ext_red_one e_invert.
Module invert := fc_invert wf weak subst.
Module unique := fc_unique wf subst.
Set Bullet Behavior "Strict Subproofs".
Set Implicit Arguments.
(* This version is just for "head reduction." *)

Lemma open_a_Conv : forall a b g,
open_tm_wrt_tm (a_Conv a g) b =
a_Conv (open_tm_wrt_tm a b) (open_co_wrt_tm g b).