X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_drops.ma;h=40ce94c71227cb3a5a72492d04311a61a63d2985;hb=75f395f0febd02de8e0f881d918a8812b1425c8d;hp=9e334565f386fc740e66a8f1bf9b6b19c905300e;hpb=d59f344b1e4b377e2f06abd9f8856d686d21b222;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
index 9e334565f..40ce94c71 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_drops.ma
@@ -20,23 +20,23 @@ include "basic_2/static/lfxs.ma".
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
 definition dedropable_sn: predicate (relation3 lenv term term) ≝
-                          λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 →
-                          ∀K2,T. K1 ⪤*[R, T] K2 → ∀U. ⬆*[f] T ≡ U →
-                          ∃∃L2. L1 ⪤*[R, U] L2 & ⬇*[b, f] L2 ≡ K2 & L1 ≐[f] L2.
+                          λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 →
+                          ∀K2,T. K1 ⪤*[R, T] K2 → ∀U. ⬆*[f] T ≘ U →
+                          ∃∃L2. L1 ⪤*[R, U] L2 & ⬇*[b, f] L2 ≘ K2 & L1 ≡[f] L2.
 
 definition dropable_sn: predicate (relation3 lenv term term) ≝
-                        λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≡ K1 → 𝐔⦃f⦄ →
-                        ∀L2,U. L1 ⪤*[R, U] L2 → ∀T. ⬆*[f] T ≡ U →
-                        ∃∃K2. K1 ⪤*[R, T] K2 & ⬇*[b, f] L2 ≡ K2.
+                        λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 → 𝐔⦃f⦄ →
+                        ∀L2,U. L1 ⪤*[R, U] L2 → ∀T. ⬆*[f] T ≘ U →
+                        ∃∃K2. K1 ⪤*[R, T] K2 & ⬇*[b, f] L2 ≘ K2.
 
 definition dropable_dx: predicate (relation3 lenv term term) ≝
                         λR. ∀L1,L2,U. L1 ⪤*[R, U] L2 →
-                        ∀b,f,K2. ⬇*[b, f] L2 ≡ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≡ U →
-                        ∃∃K1. ⬇*[b, f] L1 ≡ K1 & K1 ⪤*[R, T] K2.
+                        ∀b,f,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
+                        ∃∃K1. ⬇*[b, f] L1 ≘ K1 & K1 ⪤*[R, T] K2.
 
 definition lfxs_transitive_next: relation3 … ≝ λR1,R2,R3.
-                                 ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≡ f →
-                                 ∀g,I,K,n. ⬇*[n] L ≡ K.ⓘ{I} → ⫯g = ⫱*[n] f →
+                                 ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f →
+                                 ∀g,I,K,n. ⬇*[n] L ≘ K.ⓘ{I} → ⫯g = ⫱*[n] f →
                                  lexs_transitive (cext2 R1) (cext2 R2) (cext2 R3) (cext2 R1) cfull g K I.
 
 (* Properties with generic slicing for local environments *******************)
@@ -88,36 +88,36 @@ qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_lift_O *)
 lemma lfxs_inv_lifts_bi: ∀R,L1,L2,U. L1 ⪤*[R, U] L2 → ∀b,f. 𝐔⦃f⦄ → 
-                         ∀K1,K2. ⬇*[b, f] L1 ≡ K1 → ⬇*[b, f] L2 ≡ K2 →
-                         ∀T. ⬆*[f] T ≡ U → K1 ⪤*[R, T] K2.
+                         ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
+                         ∀T. ⬆*[f] T ≘ U → K1 ⪤*[R, T] K2.
 #R #L1 #L2 #U #HL12 #b #f #Hf #K1 #K2 #HLK1 #HLK2 #T #HTU
 elim (lfxs_dropable_sn … HLK1 … HL12 … HTU) -L1 -U // #Y #HK12 #HY
 lapply (drops_mono … HY … HLK2) -b -f -L2 #H destruct //
 qed-.
 
-lemma lfxs_inv_lref_pair_sn: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →
-                             ∃∃K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 & K1 ⪤*[R, V1] K2 & R K1 V1 V2.
+lemma lfxs_inv_lref_pair_sn: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ⪤*[R, V1] K2 & R K1 V1 V2.
 #R #L1 #L2 #i #HL12 #I #K1 #V1 #HLK1 elim (lfxs_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (lfxs_inv_zero_pair_sn … HY) -HY
 #K2 #V2 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma lfxs_inv_lref_pair_dx: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 →
-                             ∃∃K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 & K1 ⪤*[R, V1] K2 & R K1 V1 V2.
+lemma lfxs_inv_lref_pair_dx: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ⪤*[R, V1] K2 & R K1 V1 V2.
 #R #L1 #L2 #i #HL12 #I #K2 #V2 #HLK2 elim (lfxs_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (lfxs_inv_zero_pair_dx … HY) -HY
 #K1 #V1 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma lfxs_inv_lref_unit_sn: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K1. ⬇*[i] L1 ≡ K1.ⓤ{I} →
-                             ∃∃f,K2. ⬇*[i] L2 ≡ K2.ⓤ{I} & K1 ⪤*[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
+lemma lfxs_inv_lref_unit_sn: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} →
+                             ∃∃f,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} & K1 ⪤*[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
 #R #L1 #L2 #i #HL12 #I #K1 #HLK1 elim (lfxs_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (lfxs_inv_zero_unit_sn … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma lfxs_inv_lref_unit_dx: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K2. ⬇*[i] L2 ≡ K2.ⓤ{I} →
-                             ∃∃f,K1. ⬇*[i] L1 ≡ K1.ⓤ{I} & K1 ⪤*[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
+lemma lfxs_inv_lref_unit_dx: ∀R,L1,L2,i. L1 ⪤*[R, #i] L2 → ∀I,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} →
+                             ∃∃f,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} & K1 ⪤*[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
 #R #L1 #L2 #i #HL12 #I #K2 #HLK2 elim (lfxs_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (lfxs_inv_zero_unit_dx … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/