milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cny / cpye.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/cpye.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/cpye.etc
deleted file mode 100644 (file)
index 71e06ea..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cny/cpye.etc
+++ /dev/null
@@ -1,89 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/notation/relations/psubsteval_6.ma".
-include "basic_2/relocation/cny.ma".
-include "basic_2/substitution/cpys.ma".
-
-(* EVALUATION FOR CONTEXT-SENSITIVE EXTENDED SUBSTITUTION ON TERMS **********)
-
-definition cpye: ynat → ynat → relation4 genv lenv term term ≝
-                 λd,e,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 ∧ ⦃G, L⦄ ⊢ ▶[d, e] 𝐍⦃T2⦄.
-
-interpretation "evaluation for context-sensitive extended substitution (term)"
-   'PSubstEval G L T1 T2 d e = (cpye d e G L T1 T2).
-
-(* Basic_properties *********************************************************)
-
-(* Note: this should go in subconversion *)
-lemma leqy_cpye_trans: ∀G,L2,T1,T2,d,e. ⦃G, L2⦄ ⊢ T1 ▶*[d, e] 𝐍⦃T2⦄ →
-                       ∀L1. L1 ⊑×[d, e] L2 → L2 ⊑×[d, e] L1 → ⦃G, L1⦄ ⊢ T1 ▶*[d, e] 𝐍⦃T2⦄.
-#G #L2 #T1 #T2 #d #e *
-/4 width=8 by lsuby_cpys_trans, lsuby_cny_conf, conj/
-qed-.
-
-lemma cpye_sort: ∀G,L,d,e,k. ⦃G, L⦄ ⊢ ⋆k ▶*[d, e] 𝐍⦃⋆k⦄.
-/3 width=5 by cny_sort, conj/ qed.
-
-lemma cpye_free: ∀G,L,d,e,i. |L| ≤ i → ⦃G, L⦄ ⊢ #i ▶*[d, e] 𝐍⦃#i⦄.
-/3 width=6 by cny_lref_free, conj/ qed.
-
-lemma cpye_top: ∀G,L,d,e,i. d + e ≤ yinj i → ⦃G, L⦄ ⊢ #i ▶*[d, e] 𝐍⦃#i⦄.
-/3 width=6 by cny_lref_top, conj/ qed.
-
-lemma cpye_skip: ∀G,L,d,e,i. yinj i < d → ⦃G, L⦄ ⊢ #i ▶*[d, e] 𝐍⦃#i⦄.
-/3 width=6 by cny_lref_skip, conj/ qed.
-
-lemma cpye_gref: ∀G,L,d,e,p. ⦃G, L⦄ ⊢ §p ▶*[d, e] 𝐍⦃§p⦄.
-/3 width=5 by cny_gref, conj/ qed.
-
-lemma cpye_bind: ∀G,L,V1,V2,d,e. ⦃G, L⦄ ⊢ V1 ▶*[d, e] 𝐍⦃V2⦄ →
-                 ∀I,T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ▶*[⫯d, e] 𝐍⦃T2⦄ →
-                 ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ▶*[d, e] 𝐍⦃ⓑ{a,I}V2.T2⦄.
-#G #L #V1 #V2 #d #e * #HV12 #HV2 #I #T1 #T2 *
-/5 width=8 by cpys_bind, cny_bind, lsuby_cny_conf, lsuby_succ, conj/
-qed.
-
-lemma cpye_flat: ∀G,L,V1,V2,d,e. ⦃G, L⦄ ⊢ V1 ▶*[d, e] 𝐍⦃V2⦄ →
-                 ∀T1,T2. ⦃G, L⦄ ⊢ T1 ▶*[d, e] 𝐍⦃T2⦄ →
-                 ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ▶*[d, e] 𝐍⦃ⓕ{I}V2.T2⦄.
-#G #L #V1 #V2 #d #e * #HV12 #HV2 #T1 #T2 *
-/3 width=7 by cpys_flat, cny_flat, conj/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma cpye_inv_sort1: ∀G,L,X,d,e,k. ⦃G, L⦄ ⊢ ⋆k ▶*[d, e] 𝐍⦃X⦄ → X = ⋆k.
-#G #L #X #d #e #k * /2 width=5 by cpys_inv_sort1/
-qed-.
-
-lemma cpye_inv_gref1: ∀G,L,X,d,e,p. ⦃G, L⦄ ⊢ §p ▶*[d, e] 𝐍⦃X⦄ → X = §p.
-#G #L #X #d #e #p * /2 width=5 by cpys_inv_gref1/
-qed-.
-
-lemma cpye_inv_bind1: ∀a,I,G,L,V1,T1,X,d,e. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ▶*[d, e] 𝐍⦃X⦄ →
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ▶*[d, e] 𝐍⦃V2⦄ & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ▶*[⫯d, e] 𝐍⦃T2⦄ &
-                               X = ⓑ{a,I}V2.T2.
-#a #I #G #L #V1 #T1 #X #d #e * #H1 #H2 elim (cpys_inv_bind1 … H1) -H1
-#V2 #T2 #HV12 #HT12 #H destruct elim (cny_inv_bind … H2) -H2
-/5 width=8 by lsuby_cny_conf, lsuby_succ, ex3_2_intro, conj/
-qed-.
-
-lemma cpye_inv_flat1: ∀I,G,L,V1,T1,X,d,e. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ▶*[d, e] 𝐍⦃X⦄ →
-                      ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ▶*[d, e] 𝐍⦃V2⦄ & ⦃G, L⦄ ⊢ T1 ▶*[d, e] 𝐍⦃T2⦄ &
-                               X = ⓕ{I}V2.T2.
-#I #G #L #V1 #T1 #X #d #e * #H1 #H2 elim (cpys_inv_flat1 … H1) -H1
-#V2 #T2 #HV12 #HT12 #H destruct elim (cny_inv_flat … H2) -H2
-/3 width=5 by ex3_2_intro, conj/
-qed-.