update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
index 9a9df172e0c2955b90293c20b7750a1f93eda46d..4866935facc390eff0d140edd61e4172bd682565 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
@@ -25,18 +25,18 @@ definition f_dedropable_sn: predicate (relation3 lenv term term) ≝
                             ∃∃L2. L1 ⪤[R,U] L2 & ⇩*[b,f] L2 ≘ K2 & L1 ≡[f] L2.
 
 definition f_dropable_sn: predicate (relation3 lenv term term) ≝
-                          λR. â\88\80b,f,L1,K1. â\87©*[b,f] L1 â\89\98 K1 â\86\92 ð\9d\90\94â¦\83fâ¦\84 →
+                          λR. â\88\80b,f,L1,K1. â\87©*[b,f] L1 â\89\98 K1 â\86\92 ð\9d\90\94â\9dªfâ\9d« →
                           ∀L2,U. L1 ⪤[R,U] L2 → ∀T. ⇧*[f] T ≘ U →
                           ∃∃K2. K1 ⪤[R,T] K2 & ⇩*[b,f] L2 ≘ K2.
 
 definition f_dropable_dx: predicate (relation3 lenv term term) ≝
                           λR. ∀L1,L2,U. L1 ⪤[R,U] L2 →
-                          â\88\80b,f,K2. â\87©*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â¦\83fâ¦\84 → ∀T. ⇧*[f] T ≘ U →
+                          â\88\80b,f,K2. â\87©*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â\9dªfâ\9d« → ∀T. ⇧*[f] T ≘ U →
                           ∃∃K1. ⇩*[b,f] L1 ≘ K1 & K1 ⪤[R,T] K2.
 
 definition f_transitive_next: relation3 … ≝ λR1,R2,R3.
-                              â\88\80f,L,T. L â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f →
-                              ∀g,I,K,n. ⇩*[n] L ≘ K.ⓘ{I} → ↑g = ⫱*[n] f →
+                              â\88\80f,L,T. L â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f →
+                              ∀g,I,K,n. ⇩*[n] L ≘ K.ⓘ[I] → ↑g = ⫱*[n] f →
                               sex_transitive (cext2 R1) (cext2 R2) (cext2 R3) (cext2 R1) cfull g K I.
 
 (* Properties with generic slicing for local environments *******************)
@@ -90,7 +90,7 @@ qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_lift_O *)
 lemma rex_inv_lifts_bi (R):
-      â\88\80L1,L2,U. L1 ⪤[R,U] L2 â\86\92 â\88\80b,f. ð\9d\90\94â¦\83fâ¦\84 →
+      â\88\80L1,L2,U. L1 ⪤[R,U] L2 â\86\92 â\88\80b,f. ð\9d\90\94â\9dªfâ\9d« →
       ∀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
@@ -99,16 +99,16 @@ lapply (drops_mono … HY … HLK2) -b -f -L2 #H destruct //
 qed-.
 
 lemma rex_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.
+      ∀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 (rex_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (rex_inv_zero_pair_sn … HY) -HY
 #K2 #V2 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
 lemma rex_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.
+      ∀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 (rex_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (rex_inv_zero_pair_dx … HY) -HY
 #K1 #V1 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
@@ -116,8 +116,8 @@ qed-.
 
 lemma rex_inv_lref_pair_bi (R) (L1) (L2) (i):
       L1 ⪤[R,#i] L2 →
-      ∀I1,K1,V1. ⇩*[i] L1 ≘ K1.ⓑ{I1}V1 →
-      ∀I2,K2,V2. ⇩*[i] L2 ≘ K2.ⓑ{I2}V2 →
+      ∀I1,K1,V1. ⇩*[i] L1 ≘ K1.ⓑ[I1]V1 →
+      ∀I2,K2,V2. ⇩*[i] L2 ≘ K2.ⓑ[I2]V2 →
       ∧∧ K1 ⪤[R,V1] K2 & R K1 V1 V2 & I1 = I2.
 #R #L1 #L2 #i #H12 #I1 #K1 #V1 #H1 #I2 #K2 #V2 #H2
 elim (rex_inv_lref_pair_sn … H12 … H1) -L1 #Y2 #X2 #HLY2 #HK12 #HV12
@@ -126,16 +126,16 @@ lapply (drops_mono … HLY2 … H2) -HLY2 -H2 #H destruct
 qed-.
 
 lemma rex_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⦄.
+      ∀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 (rex_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (rex_inv_zero_unit_sn … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
 lemma rex_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⦄.
+      ∀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 (rex_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (rex_inv_zero_unit_dx … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/