universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
index 854a79ce6a73bc44514ab01619152415e3d54c28..adc75dd3b6c17789e0474146e8b977ee1913575f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc.ma
@@ -12,26 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lrsubeq_4.ma".
+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) (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_abbr: ∀L1,L2,V,W,A. ⦃G, L1, V⦄ ϵ[RP] 〚A〛 → ⦃G, L1, W⦄ ϵ[RP] 〚A〛 → ⦃G, L2⦄ ⊢ W ⁝ A →
+| 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)"
-  'LRSubEq RP G L1 L2 = (lsubc RP G 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: â\88\80RP,G,L1,L2. G â\8a¢ L1 â\8a\91[RP] L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubc_inv_atom1_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 → L1 = ⋆ → L2 = ⋆.
 #RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -40,30 +41,30 @@ fact lsubc_inv_atom1_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → L1 = ⋆ → L2
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_r *)
-lemma lsubc_inv_atom1: â\88\80RP,G,L2. G â\8a¢ â\8b\86 â\8a\91[RP] L2 → L2 = ⋆.
+lemma lsubc_inv_atom1: â\88\80RP,G,L2. G â\8a¢ â\8b\86 â«\83[RP] L2 → L2 = ⋆.
 /2 width=5 by lsubc_inv_atom1_aux/ qed-.
 
-fact lsubc_inv_pair1_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â\8a\91[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (â\88\83â\88\83K2. G â\8a¢ K1 â\8a\91[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+fact lsubc_inv_pair1_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (â\88\83â\88\83K2. G â\8a¢ K1 â«\83[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 â\8a¢ K1 â\8a\91[RP] K2 &
+                                      G â\8a¢ K1 â«\83[RP] K2 &
                                       L2 = K2. ⓛW & X = ⓝW.V & I = Abbr.
 #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: â\88\80RP,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\8a\91[RP] L2 →
-                       (â\88\83â\88\83K2. G â\8a¢ K1 â\8a\91[RP] K2 & L2 = K2.ⓑ{I}X) ∨
+lemma lsubc_inv_pair1: â\88\80RP,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â«\83[RP] L2 →
+                       (â\88\83â\88\83K2. G â\8a¢ K1 â«\83[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 â\8a¢ K1 â\8a\91[RP] K2 &
+                                   G â\8a¢ K1 â«\83[RP] K2 &
                                    L2 = K2.ⓛW & X = ⓝW.V & I = Abbr.
 /2 width=3 by lsubc_inv_pair1_aux/ qed-.
 
-fact lsubc_inv_atom2_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â\8a\91[RP] L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubc_inv_atom2_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 → L2 = ⋆ → L1 = ⋆.
 #RP #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -72,34 +73,40 @@ fact lsubc_inv_atom2_aux: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → L2 = ⋆ → L1
 qed-.
 
 (* Basic_1: was just: csubc_gen_sort_l *)
-lemma lsubc_inv_atom2: â\88\80RP,G,L1. G â\8a¢ L1 â\8a\91[RP] ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: â\88\80RP,G,L1. G â\8a¢ L1 â«\83[RP] ⋆ → L1 = ⋆.
 /2 width=5 by lsubc_inv_atom2_aux/ qed-.
 
-fact lsubc_inv_pair2_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â\8a\91[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{I} W →
-                          (â\88\83â\88\83K1. G â\8a¢ K1 â\8a\91[RP] K2 & L1 = K1. ⓑ{I} W) ∨
+fact lsubc_inv_pair2_aux: â\88\80RP,G,L1,L2. G â\8a¢ L1 â«\83[RP] L2 → ∀I,K2,W. L2 = K2.ⓑ{I} W →
+                          (â\88\83â\88\83K1. G â\8a¢ K1 â«\83[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 â\8a¢ K1 â\8a\91[RP] K2 &
+                                    G â\8a¢ K1 â«\83[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: â\88\80RP,I,G,L1,K2,W. G â\8a¢ L1 â\8a\91[RP] K2.ⓑ{I} W →
-                       (â\88\83â\88\83K1. G â\8a¢ K1 â\8a\91[RP] K2 & L1 = K1.ⓑ{I} W) ∨
+lemma lsubc_inv_pair2: â\88\80RP,I,G,L1,K2,W. G â\8a¢ L1 â«\83[RP] K2.ⓑ{I} W →
+                       (â\88\83â\88\83K1. G â\8a¢ K1 â«\83[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 â\8a¢ K1 â\8a\91[RP] K2 &
+                                 G â\8a¢ K1 â«\83[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: â\88\80RP,G,L. G â\8a¢ L â\8a\91[RP] L.
-#RP #G #L elim L -L // /2 width=1/
+lemma lsubc_refl: â\88\80RP,G,L. G â\8a¢ L â«\83[RP] L.
+#RP #G #L elim L -L /2 width=1 by lsubc_pair/
 qed.
 
 (* Basic_1: removed theorems 3: