X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flsubc.ma;h=adc75dd3b6c17789e0474146e8b977ee1913575f;hb=fca909e9e53de73771e1b47e94434ae8f747d7fb;hp=a3cc36b24dc0465539348458c456ad3b323be051;hpb=f62eeb3c7824564ccbe4fff6e75ddee46ca39cc0;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
index a3cc36b24..adc75dd3b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
@@ -12,26 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/lrsubeqc_4.ma".
+include "basic_2/static/lsubr.ma".
 include "basic_2/static/aaa.ma".
-include "basic_2/computation/acp_cr.ma".
+include "basic_2/computation/gcp_cr.ma".
 
-(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
+(* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC 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⦄ ϵ[RP] 〚A〛 → ⦃L1, W⦄ ϵ[RP] 〚A〛 → L2 ⊢ W ⁝ A →
-              lsubc RP L1 L2 → lsubc RP (L1. ⓓⓝW.V) (L2. ⓛW)
+inductive lsubc (RP) (G): relation lenv ≝
+| lsubc_atom: lsubc RP G (⋆) (⋆)
+| lsubc_pair: ∀I,L1,L2,V. lsubc RP G L1 L2 → lsubc RP G (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| 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 (abstract candidates of reducibility)"
-  'CrSubEq L1 RP L2 = (lsubc RP L1 L2).
+  "local environment refinement (generic reducibility)"
+  'LRSubEqC RP G L1 L2 = (lsubc RP G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
-#RP #L1 #L2 * -L1 -L2
+fact lsubc_inv_atom1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → L1 = ⋆ → L2 = ⋆.
+#RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
@@ -39,31 +41,31 @@ fact lsubc_inv_atom1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L1 = ⋆ → L2 = ⋆.
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: ∀RP,L2. ⋆ ⊑[RP] L2 → L2 = ⋆.
-/2 width=4 by lsubc_inv_atom1_aux/ qed-.
+lemma lsubc_inv_atom1: ∀RP,G,L2. G ⊢ ⋆ ⫃[RP] L2 → L2 = ⋆.
+/2 width=5 by lsubc_inv_atom1_aux/ qed-.
 
-fact lsubc_inv_pair1_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (∃∃K2. K1 ⊑[RP] K2 & L2 = K2. ⓑ{I}X) ∨
-                          ∃∃K2,V,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                      K1 ⊑[RP] K2 &
+fact lsubc_inv_pair1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+                          ∃∃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 & X = ⓝW.V & I = Abbr.
-#RP #L1 #L2 * -L1 -L2
+#RP #G #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 #H1W2 #H2W2 #HL12 #I #K1 #V #H destruct /3 width=10/
+| #J #L1 #L2 #V #HL12 #I #K1 #W #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K1 #V #H destruct /3 width=10 by ex7_4_intro, or_intror/
 ]
 qed-.
 
 (* Basic_1: was: csubc_gen_head_r *)
-lemma lsubc_inv_pair1: ∀RP,I,K1,L2,X. K1.ⓑ{I}X ⊑[RP] L2 →
-                       (∃∃K2. K1 ⊑[RP] K2 & L2 = K2.ⓑ{I}X) ∨
-                       ∃∃K2,V,W,A. ⦃K1, V⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                   K1 ⊑[RP] K2 &
-                                   L2 = K2. ⓛW & X = ⓝW.V & I = Abbr.
+lemma lsubc_inv_pair1: ∀RP,I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⫃[RP] L2 →
+                       (∃∃K2. G ⊢ K1 ⫃[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+                       ∃∃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 & X = ⓝW.V & I = Abbr.
 /2 width=3 by lsubc_inv_pair1_aux/ qed-.
 
-fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
-#RP #L1 #L2 * -L1 -L2
+fact lsubc_inv_atom2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → L2 = ⋆ → L1 = ⋆.
+#RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #V #W #A #_ #_ #_ #_ #H destruct
@@ -71,34 +73,40 @@ fact lsubc_inv_atom2_aux: ∀RP,L1,L2. L1 ⊑[RP] L2 → L2 = ⋆ → L1 = ⋆.
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: ∀RP,L1. L1 ⊑[RP] ⋆ → L1 = ⋆.
-/2 width=4 by lsubc_inv_atom2_aux/ 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⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                    K1 ⊑[RP] K2 &
-                                    L1 = K1. ⓓⓝW.V & I = Abst.
-#RP #L1 #L2 * -L1 -L2
+lemma lsubc_inv_atom2: ∀RP,G,L1. G ⊢ L1 ⫃[RP] ⋆ → L1 = ⋆.
+/2 width=5 by lsubc_inv_atom2_aux/ qed-.
+
+fact lsubc_inv_pair2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{I} W →
+                          (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1. ⓑ{I} W) ∨
+                          ∃∃K1,V,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 = Abst.
+#RP #G #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 #H1W2 #H2W2 #HL12 #I #K2 #W #H destruct /3 width=8/
+| #J #L1 #L2 #V #HL12 #I #K2 #W #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #V1 #W2 #A #HV1 #H1W2 #H2W2 #HL12 #I #K2 #W #H destruct /3 width=8 by ex6_3_intro, or_intror/
 ]
 qed-.
 
 (* Basic_1: was just: 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⦄ ϵ[RP] 〚A〛 & ⦃K1, W⦄ ϵ[RP] 〚A〛 & K2 ⊢ W ⁝ A &
-                                 K1 ⊑[RP] K2 &
+lemma lsubc_inv_pair2: ∀RP,I,G,L1,K2,W. G ⊢ L1 ⫃[RP] K2.ⓑ{I} W →
+                       (∃∃K1. G ⊢ K1 ⫃[RP] K2 & L1 = K1.ⓑ{I} W) ∨
+                       ∃∃K1,V,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 = Abst.
 /2 width=3 by lsubc_inv_pair2_aux/ qed-.
 
+(* Basic forward lemmas *****************************************************)
+
+lemma lsubc_fwd_lsubr: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 → L1 ⫃ L2.
+#RP #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_pair, lsubr_beta/
+qed-.
+
 (* Basic properties *********************************************************)
 
 (* Basic_1: was just: csubc_refl *)
-lemma lsubc_refl: ∀RP,L. L ⊑[RP] L.
-#RP #L elim L -L // /2 width=1/
+lemma lsubc_refl: ∀RP,G,L. G ⊢ L ⫃[RP] L.
+#RP #G #L elim L -L /2 width=1 by lsubc_pair/
 qed.
 
 (* Basic_1: removed theorems 3: