notational change of lift, drop, and gget

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / cpy_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_lift.ma
index 78318917befb3801cfd6b55eb37eea554edcf100..991d4db29badad333a60668aeb46eb1a1a19058b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_lift.ma
@@ -21,8 +21,8 @@ include "basic_2/substitution/cpy.ma".
 
 (* Basic_1: was: subst1_lift_lt *)
 lemma cpy_lift_le: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶[dt, et] T2 →
-                   â\88\80L,U1,U2,s,d,e. â\87©[s, d, e] L ≡ K →
-                   â\87§[d, e] T1 â\89¡ U1 â\86\92 â\87§[d, e] T2 ≡ U2 →
+                   â\88\80L,U1,U2,s,d,e. â¬\87[s, d, e] L ≡ K →
+                   â¬\86[d, e] T1 â\89¡ U1 â\86\92 â¬\86[d, e] T2 ≡ U2 →
                    dt + et ≤ d → ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2.
 #G #K #T1 #T2 #dt #et #H elim H -G -K -T1 -T2 -dt -et
 [ #I #G #K #dt #et #L #U1 #U2 #s #d #e #_ #H1 #H2 #_
@@ -47,8 +47,8 @@ lemma cpy_lift_le: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶[dt, et] T2 →
 qed-.
 
 lemma cpy_lift_be: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶[dt, et] T2 →
-                   â\88\80L,U1,U2,s,d,e. â\87©[s, d, e] L ≡ K →
-                   â\87§[d, e] T1 â\89¡ U1 â\86\92 â\87§[d, e] T2 ≡ U2 →
+                   â\88\80L,U1,U2,s,d,e. â¬\87[s, d, e] L ≡ K →
+                   â¬\86[d, e] T1 â\89¡ U1 â\86\92 â¬\86[d, e] T2 ≡ U2 →
                    dt ≤ d → d ≤ dt + et → ⦃G, L⦄ ⊢ U1 ▶[dt, et + e] U2.
 #G #K #T1 #T2 #dt #et #H elim H -G -K -T1 -T2 -dt -et
 [ #I #G #K #dt #et #L #U1 #U2 #s #d #e #_ #H1 #H2 #_ #_
@@ -81,8 +81,8 @@ qed-.
 
 (* Basic_1: was: subst1_lift_ge *)
 lemma cpy_lift_ge: ∀G,K,T1,T2,dt,et. ⦃G, K⦄ ⊢ T1 ▶[dt, et] T2 →
-                   â\88\80L,U1,U2,s,d,e. â\87©[s, d, e] L ≡ K →
-                   â\87§[d, e] T1 â\89¡ U1 â\86\92 â\87§[d, e] T2 ≡ U2 →
+                   â\88\80L,U1,U2,s,d,e. â¬\87[s, d, e] L ≡ K →
+                   â¬\86[d, e] T1 â\89¡ U1 â\86\92 â¬\86[d, e] T2 ≡ U2 →
                    d ≤ dt → ⦃G, L⦄ ⊢ U1 ▶[dt+e, et] U2.
 #G #K #T1 #T2 #dt #et #H elim H -G -K -T1 -T2 -dt -et
 [ #I #G #K #dt #et #L #U1 #U2 #s #d #e #_ #H1 #H2 #_
@@ -109,9 +109,9 @@ qed-.
 
 (* Basic_1: was: subst1_gen_lift_lt *)
 lemma cpy_inv_lift1_le: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                        â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                        â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                         dt + et ≤ d →
-                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, et] T2 & â\87§[d, e] T2 ≡ U2.
+                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, et] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #H elim H -G -L -U1 -U2 -dt -et
 [ * #i #G #L #dt #et #K #s #d #e #_ #T1 #H #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3 by ex2_intro/
@@ -138,9 +138,9 @@ lemma cpy_inv_lift1_le: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
 qed-.
 
 lemma cpy_inv_lift1_be: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                        â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                        â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                         dt ≤ d → yinj d + e ≤ dt + et →
-                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, et-e] T2 & â\87§[d, e] T2 ≡ U2.
+                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, et-e] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #H elim H -G -L -U1 -U2 -dt -et
 [ * #i #G #L #dt #et #K #s #d #e #_ #T1 #H #_ #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3 by ex2_intro/
@@ -178,9 +178,9 @@ qed-.
 
 (* Basic_1: was: subst1_gen_lift_ge *)
 lemma cpy_inv_lift1_ge: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                        â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                        â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                         yinj d + e ≤ dt →
-                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt-e, et] T2 & â\87§[d, e] T2 ≡ U2.
+                        â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt-e, et] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #H elim H -G -L -U1 -U2 -dt -et
 [ * #i #G #L #dt #et #K #s #d #e #_ #T1 #H #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3 by ex2_intro/
@@ -215,9 +215,9 @@ qed-.
 (* Advanced inversion lemmas on relocation ***********************************)
 
 lemma cpy_inv_lift1_ge_up: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                           â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                           â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                            d ≤ dt → dt ≤ yinj d + e → yinj d + e ≤ dt + et →
-                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[d, dt + et - (yinj d + e)] T2 & â\87§[d, e] T2 ≡ U2.
+                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[d, dt + et - (yinj d + e)] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #HU12 #K #s #d #e #HLK #T1 #HTU1 #Hddt #Hdtde #Hdedet
 elim (cpy_split_up … HU12 (d + e)) -HU12 // -Hdedet #U #HU1 #HU2
 lapply (cpy_weak … HU1 d e ? ?) -HU1 // [ >ymax_pre_sn_comm // ] -Hddt -Hdtde #HU1
@@ -226,9 +226,9 @@ elim (cpy_inv_lift1_ge … HU2 … HLK … HTU1) -U -L /2 width=3 by ex2_intro/
 qed-.
 
 lemma cpy_inv_lift1_be_up: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                           â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                           â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                            dt ≤ d → dt + et ≤ yinj d + e →
-                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, d-dt] T2 & â\87§[d, e] T2 ≡ U2.
+                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, d-dt] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #HU12 #K #s #d #e #HLK #T1 #HTU1 #Hdtd #Hdetde
 lapply (cpy_weak … HU12 dt (d+e-dt) ? ?) -HU12 //
 [ >ymax_pre_sn_comm /2 width=1 by yle_plus_dx1_trans/ ] -Hdetde #HU12
@@ -236,9 +236,9 @@ elim (cpy_inv_lift1_be … HU12 … HLK … HTU1) -U1 -L /2 width=3 by ex2_intro
 qed-.
 
 lemma cpy_inv_lift1_le_up: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶[dt, et] U2 →
-                           â\88\80K,s,d,e. â\87©[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 →
+                           â\88\80K,s,d,e. â¬\87[s, d, e] L â\89¡ K â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 →
                            dt ≤ d → d ≤ dt + et → dt + et ≤ yinj d + e →
-                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, d - dt] T2 & â\87§[d, e] T2 ≡ U2.
+                           â\88\83â\88\83T2. â¦\83G, Kâ¦\84 â\8a¢ T1 â\96¶[dt, d - dt] T2 & â¬\86[d, e] T2 ≡ U2.
 #G #L #U1 #U2 #dt #et #HU12 #K #s #d #e #HLK #T1 #HTU1 #Hdtd #Hddet #Hdetde
 elim (cpy_split_up … HU12 d) -HU12 // #U #HU1 #HU2
 elim (cpy_inv_lift1_le … HU1 … HLK … HTU1) -U1