X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Flsubsv.ma;h=0d39f32ec5d375d4f56b1928381111ff936c60eb;hb=d7ccf1bd91637d3c59a285df6f215ecfde2a2450;hp=29d6151fe877e584e1ccb65efa0c1caa6fc5cd8c;hpb=cac628104788b9400cc1a33407272fd4c35f2402;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
index 29d6151fe..0d39f32ec 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
@@ -12,104 +12,104 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lrsubeqv_4.ma".
+include "basic_2/notation/relations/lrsubeqv_5.ma".
 include "basic_2/dynamic/snv.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
 
 (* Note: this is not transitive *)
-inductive lsubsv (h:sh) (g:sd h): relation lenv ≝
-| lsubsv_atom: lsubsv h g (⋆) (⋆)
-| lsubsv_pair: ∀I,L1,L2,V. lsubsv h g L1 L2 →
-               lsubsv h g (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubsv_abbr: ∀L1,L2,W,V,W1,V2,l. ⦃h, L1⦄ ⊢ ⓝW.V ¡[h, g] → ⦃h, L2⦄ ⊢ W ¡[h, g] →
-               ⦃h, L1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ → ⦃h, L2⦄ ⊢ W •[h, g] ⦃l, V2⦄ →
-               lsubsv h g L1 L2 → lsubsv h g (L1.ⓓⓝW.V) (L2.ⓛW)
+inductive lsubsv (h) (g) (G): relation lenv ≝
+| lsubsv_atom: lsubsv h g G (⋆) (⋆)
+| lsubsv_pair: ∀I,L1,L2,V. lsubsv h g G L1 L2 →
+               lsubsv h g G (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| lsubsv_abbr: ∀L1,L2,W,V,W1,V2,l. ⦃G, L1⦄ ⊢ ⓝW.V ¡[h, g] → ⦃G, L2⦄ ⊢ W ¡[h, g] →
+               ⦃G, L1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ → ⦃G, L2⦄ ⊢ W •[h, g] ⦃l, V2⦄ →
+               lsubsv h g G L1 L2 → lsubsv h g G (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
   "local environment refinement (stratified native validity)"
-  'LRSubEqV h g L1 L2 = (lsubsv h g L1 L2).
+  'LRSubEqV h g G L1 L2 = (lsubsv h g G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubsv_inv_atom1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L1 = ⋆ → L2 = ⋆.
-#h #g #L1 #L2 * -L1 -L2
+fact lsubsv_inv_atom1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → L1 = ⋆ → L2 = ⋆.
+#h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #W #V #V1 #V2 #l #_ #_ #_ #_ #_ #H destruct
 ]
 qed-.
 
-lemma lsubsv_inv_atom1: ∀h,g,L2. h ⊢ ⋆ ¡⊑[h, g] L2 → L2 = ⋆.
-/2 width=5 by lsubsv_inv_atom1_aux/ qed-.
+lemma lsubsv_inv_atom1: ∀h,g,G,L2. G ⊢ ⋆ ¡⊑[h, g] L2 → L2 = ⋆.
+/2 width=6 by lsubsv_inv_atom1_aux/ qed-.
 
-fact lsubsv_inv_pair1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
+fact lsubsv_inv_pair1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 →
                            ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                           (∃∃K2. h ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
-                           ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
-                                             ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
-                                             h ⊢ K1 ¡⊑[h, g] K2 &
+                           (∃∃K2. G ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                           ∃∃K2,W,V,W1,V2,l. ⦃G, K1⦄ ⊢ X ¡[h, g] & ⦃G, K2⦄ ⊢ W ¡[h, g] &
+                                             ⦃G, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃G, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                             G ⊢ K1 ¡⊑[h, g] K2 &
                                              I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
-#h #g #L1 #L2 * -L1 -L2
+#h #g #G #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
 | #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3/
 | #L1 #L2 #W #V #W1 #V2 #l #HV #HW #HW1 #HV2 #HL12 #J #K1 #X #H destruct /3 width=12/
 ]
 qed-.
 
-lemma lsubsv_inv_pair1: ∀h,g,I,K1,L2,X. h ⊢ K1.ⓑ{I}X ¡⊑[h, g] L2 →
-                        (∃∃K2. h ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
-                        ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
-                                          ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
-                                          h ⊢ K1 ¡⊑[h, g] K2 &
+lemma lsubsv_inv_pair1: ∀h,g,I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ¡⊑[h, g] L2 →
+                        (∃∃K2. G ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                        ∃∃K2,W,V,W1,V2,l. ⦃G, K1⦄ ⊢ X ¡[h, g] & ⦃G, K2⦄ ⊢ W ¡[h, g] &
+                                          ⦃G, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃G, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                          G ⊢ K1 ¡⊑[h, g] K2 &
                                           I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsubsv_inv_pair1_aux/ qed-.
 
-fact lsubsv_inv_atom2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L2 = ⋆ → L1 = ⋆.
-#h #g #L1 #L2 * -L1 -L2
+fact lsubsv_inv_atom2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → L2 = ⋆ → L1 = ⋆.
+#h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
 | #L1 #L2 #W #V #V1 #V2 #l #_ #_ #_ #_ #_ #H destruct
 ]
 qed-.
 
-lemma lsubsv_inv_atom2: ∀h,g,L1. h ⊢ L1 ¡⊑[h, g] ⋆ → L1 = ⋆.
-/2 width=5 by lsubsv_inv_atom2_aux/ qed-.
+lemma lsubsv_inv_atom2: ∀h,g,G,L1. G ⊢ L1 ¡⊑[h, g] ⋆ → L1 = ⋆.
+/2 width=6 by lsubsv_inv_atom2_aux/ qed-.
 
-fact lsubsv_inv_pair2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
+fact lsubsv_inv_pair2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 →
                            ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                           (∃∃K1. h ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
-                           ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
-                                           ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
-                                           h ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
-#h #g #L1 #L2 * -L1 -L2
+                           (∃∃K1. G ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                           ∃∃K1,V,W1,V2,l. ⦃G, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃G, K2⦄ ⊢ W ¡[h, g] &
+                                           ⦃G, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃G, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                           G ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+#h #g #G #L1 #L2 * -L1 -L2
 [ #J #K2 #U #H destruct
 | #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3/
 | #L1 #L2 #W #V #W1 #V2 #l #HV #HW #HW1 #HV2 #HL12 #J #K2 #U #H destruct /3 width=10/
 ]
 qed-.
 
-lemma lsubsv_inv_pair2: ∀h,g,I,L1,K2,W. h ⊢ L1 ¡⊑[h, g] K2.ⓑ{I}W →
-                        (∃∃K1. h ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
-                        ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
-                                        ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
-                                        h ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+lemma lsubsv_inv_pair2: ∀h,g,I,G,L1,K2,W. G ⊢ L1 ¡⊑[h, g] K2.ⓑ{I}W →
+                        (∃∃K1. G ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                        ∃∃K1,V,W1,V2,l. ⦃G, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃G, K2⦄ ⊢ W ¡[h, g] &
+                                        ⦃G, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃G, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                        G ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 /2 width=3 by lsubsv_inv_pair2_aux/ qed-.
 
 (* Basic_forward lemmas *****************************************************)
 
-lemma lsubsv_fwd_lsubr: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L1 ⊑ L2.
-#h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
+lemma lsubsv_fwd_lsubr: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → L1 ⊑ L2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubsv_refl: ∀h,g,L. h ⊢ L ¡⊑[h, g] L.
-#h #g #L elim L -L // /2 width=1/
+lemma lsubsv_refl: ∀h,g,G,L. G ⊢ L ¡⊑[h, g] L.
+#h #g #G #L elim L -L // /2 width=1/
 qed.
 
-lemma lsubsv_cprs_trans: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
-                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
-/3 width=5 by lsubsv_fwd_lsubr, lsubr_cprs_trans/
+lemma lsubsv_cprs_trans: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 →
+                         ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ➡* T2 → ⦃G, L1⦄ ⊢ T1 ➡* T2.
+/3 width=6 by lsubsv_fwd_lsubr, lsubr_cprs_trans/
 qed-.