]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/substitution/fqup_lleq.ma
582888e21360a5085d65decfd8b2dfa85f5445d0
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / fqup_lleq.ma
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/relocation/fqu_lleq.ma".
16 include "basic_2/substitution/fqup.ma".
17
18 (* PLUS-ITERATED SUPCLOSURE *************************************************)
19
20 (* Properties on lazy equivalence for local environments ********************)
21
22 lemma lleq_fqup_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃+ ⦃G2, K2, U⦄ →
23                        ∀L1. L1 ⋕[0, T] L2 →
24                        ∃∃K1. ⦃G1, L1, T⦄ ⊃+ ⦃G2, K1, U⦄ & K1 ⋕[0, U] K2.
25 #G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
26 [ #G2 #K2 #U #HTU #L1 #HL12 elim (lleq_fqu_trans … HTU … HL12) -L2
27   /3 width=3 by fqu_fqup, ex2_intro/
28 | #G #G2 #K #K2 #U #U2 #_ #HU2 #IHTU #L1 #HL12 elim (IHTU … HL12) -L2
29   #K1 #HTU #HK1 elim (lleq_fqu_trans … HU2 … HK1) -K
30   /3 width=5 by fqup_strap1, ex2_intro/
31 ]
32 qed-.