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(** * Regularity                                                         *)
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(** To be fully confident about the exist-fresh rules, we can show their "regularity" --- that these relations only include locally closed terms. (For the exists-fresh definition of local closure.) *)

(** Take-home exercise. [open_abs] is the analogue of subst_lc for bound variable substitution. HINT: use inversion, subst_intro and subst_lc to prove this lemma. **)
Lemma open_abs : forall e u T1,
lc (abs T1 e) ->
lc u ->
lc (open e u).