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[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / lsubc.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/static/aaa.ma".
-include "Basic_2/computation/acp_cr.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
-
-inductive lsubc (RP:lenv→predicate term): relation lenv ≝
-| lsubc_atom: lsubc RP (⋆) (⋆)
-| lsubc_pair: ∀I,L1,L2,V. lsubc RP L1 L2 → lsubc RP (L1. ⓑ{I} V) (L2. ⓑ{I} V)
-| lsubc_abbr: ∀L1,L2,V,W,A. ⦃L1, V⦄ [RP] ϵ 〚A〛 → L2 ⊢ W ÷ A →
-              lsubc RP L1 L2 → lsubc RP (L1. ⓓV) (L2. ⓛW)
-.
-
-interpretation
-  "local environment refinement (abstract candidates of reducibility)"
-  'CrSubEq L1 RP L2 = (lsubc RP L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L1 = ⋆ → L2 = ⋆.
-#RP #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #H destruct
-]
-qed.
-
-(* Basic_1: was: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: ∀RP,L2. ⋆ [RP] ⊑ L2 → L2 = ⋆.
-/2 width=4/ qed-.
-
-fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K1,V. L1 = K1. ⓑ{I} V →
-                          (∃∃K2. K1 [RP] ⊑ K2 & L2 = K2. ⓑ{I} V) ∨
-                          ∃∃K2,W,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                    K1 [RP] ⊑ K2 &
-                                    L2 = K2. ⓛW & I = Abbr.
-#RP #L1 #L2 * -L1 -L2
-[ #I #K1 #V #H destruct
-| #J #L1 #L2 #V #HL12 #I #K1 #W #H destruct /3 width=3/
-| #L1 #L2 #V1 #W2 #A #HV1 #HW2 #HL12 #I #K1 #V #H destruct /3 width=7/
-]
-qed.
-
-(* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_pair1: ∀RP,I,K1,L2,V. K1. ⓑ{I} V [RP] ⊑ L2 →
-                       (∃∃K2. K1 [RP] ⊑ K2 & L2 = K2. ⓑ{I} V) ∨
-                       ∃∃K2,W,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                 K1 [RP] ⊑ K2 &
-                                 L2 = K2. ⓛW & I = Abbr.
-/2 width=3/ qed-.
-
-fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → L2 = ⋆ → L1 = ⋆.
-#RP #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #V #W #A #_ #_ #_ #H destruct
-]
-qed.
-
-(* Basic_1: was: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: ∀RP,L1. L1 [RP] ⊑ ⋆ → L1 = ⋆.
-/2 width=4/ qed-.
-
-fact lsubc_inv_pair2_aux: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀I,K2,W. L2 = K2. ⓑ{I} W →
-                          (∃∃K1. K1 [RP] ⊑ K2 & L1 = K1. ⓑ{I} W) ∨
-                          ∃∃K1,V,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                    K1 [RP] ⊑ K2 &
-                                    L1 = K1. ⓓV & I = Abst.
-#RP #L1 #L2 * -L1 -L2
-[ #I #K2 #W #H destruct
-| #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3/
-| #L1 #L2 #V1 #W2 #A #HV1 #HW2 #HL12 #I #K2 #W #H destruct /3 width=7/
-]
-qed.
-
-(* Basic_1: was: csubc_gen_head_l *)
-lemma lsubc_inv_pair2: ∀RP,I,L1,K2,W. L1 [RP] ⊑ K2. ⓑ{I} W →
-                       (∃∃K1. K1 [RP] ⊑ K2 & L1 = K1. ⓑ{I} W) ∨
-                       ∃∃K1,V,A. ⦃K1, V⦄ [RP] ϵ 〚A〛 & K2 ⊢ W ÷ A &
-                                 K1 [RP] ⊑ K2 &
-                                 L1 = K1. ⓓV & I = Abst.
-/2 width=3/ qed-.
-
-(* Basic properties *********************************************************)
-
-(* Basic_1: was: csubc_refl *)
-lemma lsubc_refl: ∀RP,L. L [RP] ⊑ L.
-#RP #L elim L -L // /2 width=1/
-qed.
-
-(* Basic_1: removed theorems 2: csubc_clear_conf csubc_getl_conf *)