(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

include "basic_2/rt_conversion/cpce.ma".
include "basic_2/dynamic/cnv_preserve.ma".

(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)

theorem cnv_cpce_mono (a) (h) (G) (L) (T):
        ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ⦃G,L⦄ ⊢ T ![a,h] →
        ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
#h #G #L #T @(fqup_wf_ind (Ⓣ) … G L T) -G -L -T
#G0 #L0 #T0 #IH #T1
@(insert_eq_0 … G0) #G
@(insert_eq_0 … L0) #L
@(insert_eq_0 … T0) #T
* -G -L -T
[ #G #L1 #s #_ #_ #_ #_ #L2 #_ //