X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fcomputation%2Flsubc.ma;h=e61c2081d7dd66b79011c52783f58ee126e54809;hb=44c1079dabf1d3c0b69d0155ddbaea8627ec901c;hp=8cf302dc8a7645063ce55c2e7c51d185616e8144;hpb=35653f628dc3a3e665fee01acc19c660c9d555e3;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
index 8cf302dc8..e61c2081d 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma
@@ -12,25 +12,93 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "Basic_2/static/aaa.ma".
 include "Basic_2/computation/acp_cr.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
 
-inductive lsubc (R:lenv→predicate term) : relation lenv ≝
-| lsubc_atom: lsubc R (⋆) (⋆)
-| lsubc_pair: ∀I,L1,L2,V. lsubc R L1 L2 → lsubc R (L1. 𝕓{I} V) (L2. 𝕓{I} V)
-| lsubc_abbr: ∀L1,L2,V,W,A. R ⊢ {L1, V} ϵ 〚A〛 → R ⊢ {L2, W} ϵ 〚A〛 →
-              lsubc R L1 L2 → lsubc R (L1. 𝕓{Abbr} V) (L2. 𝕓{Abst} W)
+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 R L2 = (lsubc R L1 L2).
+  '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 *********************************************************)
 
-lemma lsubc_refl: ∀R,L. L [R] ⊑ L.
-#R #L elim L -L // /2 width=1/
+(* Basic_1: was: csubc_refl *)
+lemma lsubc_refl: ∀RP,L. L [RP] ⊑ L.
+#RP #L elim L -L // /2 width=1/
 qed.
 
-(* Basic inversion lemmas ***************************************************)
+(* Basic_1: removed theorems 2: csubc_clear_conf csubc_getl_conf *)