Qed.

Lemma bind_map_tm_subst_tm_sort: forall c F A B T x a,
binds c (Co (Eq A B T)) F ->
binds c (Co (Eq (tm_subst_tm_tm a x A)
(tm_subst_tm_tm a x B) (tm_subst_tm_tm a x T))) (map (tm_subst_tm_sort a x) F).