syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubc.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubc.ma
deleted file mode 100644 (file)
index bb4b27f..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubc.ma
+++ /dev/null
@@ -1,109 +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/lrsubeqc_4.ma".
-include "basic_2/static/aaa.ma".
-include "basic_2/static/gcp_cr.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
-
-inductive lsubc (RP) (G): relation lenv ≝
-| lsubc_atom: lsubc RP G (⋆) (⋆)
-| lsubc_bind: ∀I,L1,L2. lsubc RP G L1 L2 → lsubc RP G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsubc_beta: ∀L1,L2,V,W,A. ⦃G, L1, V⦄ ϵ[RP] 〚A〛 → ⦃G, L1, W⦄ ϵ[RP] 〚A〛 → ⦃G, L2⦄ ⊢ W ⁝ A →
-              lsubc RP G L1 L2 → lsubc RP G (L1. ⓓⓝW.V) (L2.ⓛW)
-.
-
-interpretation
-  "local environment refinement (generic reducibility)"
-  'LRSubEqC RP G L1 L2 = (lsubc RP G L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsubc_inv_atom1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → L1 = ⋆ → L2 = ⋆.
-#RP #G #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
-]
-qed-.
-
-(* Basic_1: was just: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: ∀RP,G,L2. G ⊢ ⋆ ⫃[RP] L2 → L2 = ⋆.
-/2 width=5 by lsubc_inv_atom1_aux/ qed-.
-
-fact lsubc_inv_bind1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K1. L1 = K1.ⓘ{I} →
-                          (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ{I}) ∨
-                          ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G ⊢ K1 ⫃[RP] K2 &
-                                      L2 = K2. ⓛW & I = BPair Abbr (ⓝW.V).
-#RP #G #L1 #L2 * -L1 -L2
-[ #I #K1 #H destruct
-| #J #L1 #L2 #HL12 #I #K1 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K1 #H destruct
-  /3 width=10 by ex6_4_intro, or_intror/
-]
-qed-.
-
-(* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_bind1: ∀RP,I,G,K1,L2. G ⊢ K1.ⓘ{I} ⫃[RP] L2 →
-                       (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓘ{I}) ∨
-                       ∃∃K2,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                   G ⊢ K1 ⫃[RP] K2 &
-                                   L2 = K2.ⓛW & I = BPair Abbr (ⓝW.V).
-/2 width=3 by lsubc_inv_bind1_aux/ qed-.
-
-fact lsubc_inv_atom2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → L2 = ⋆ → L1 = ⋆.
-#RP #G #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
-]
-qed-.
-
-(* Basic_1: was just: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: ∀RP,G,L1. G ⊢ L1 ⫃[RP] ⋆ → L1 = ⋆.
-/2 width=5 by lsubc_inv_atom2_aux/ qed-.
-
-fact lsubc_inv_bind2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K2. L2 = K2.ⓘ{I} →
-                          (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1. ⓘ{I}) ∨
-                          ∃∃K1,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G ⊢ K1 ⫃[RP] K2 &
-                                      L1 = K1.ⓓⓝW.V & I = BPair Abst W.
-#RP #G #L1 #L2 * -L1 -L2
-[ #I #K2 #H destruct
-| #J #L1 #L2 #HL12 #I #K2 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K2 #H destruct
-  /3 width=10 by ex6_4_intro, or_intror/
-]
-qed-.
-
-(* Basic_1: was just: csubc_gen_head_l *)
-lemma lsubc_inv_bind2: ∀RP,I,G,L1,K2. G ⊢ L1 ⫃[RP] K2.ⓘ{I} →
-                       (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1.ⓘ{I}) ∨
-                       ∃∃K1,V,W,A. ⦃G, K1, V⦄ ϵ[RP] 〚A〛 & ⦃G, K1, W⦄ ϵ[RP] 〚A〛 & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                   G ⊢ K1 ⫃[RP] K2 &
-                                   L1 = K1.ⓓⓝW.V & I = BPair Abst W.
-/2 width=3 by lsubc_inv_bind2_aux/ qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was just: csubc_refl *)
-lemma lsubc_refl: ∀RP,G,L. G ⊢ L ⫃[RP] L.
-#RP #G #L elim L -L /2 width=1 by lsubc_bind/
-qed.
-
-(* Basic_1: removed theorems 3:
-            csubc_clear_conf csubc_getl_conf csubc_csuba
-*)