update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
index bc5a7056babb2ba2b28e75aa6627e699554963f0..37c629351f1c30b64f19adb8ee78124871942f2a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
@@ -21,8 +21,8 @@ include "static_2/static/frees_fqup.ma".
 (* Advanced properties ******************************************************)
 
 lemma frees_atom_drops:
-      â\88\80b,L,i. â\87©*[b,ð\9d\90\94â\9d´iâ\9dµ] L ≘ ⋆ →
-      â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L â\8a¢ ð\9d\90\85+â¦\83#iâ¦\84 ≘ ⫯*[i]↑f.
+      â\88\80b,L,i. â\87©*[b,ð\9d\90\94â\9d¨iâ\9d©] L ≘ ⋆ →
+      â\88\80f. ð\9d\90\88â\9dªfâ\9d« â\86\92 L â\8a¢ ð\9d\90\85+â\9dª#iâ\9d« ≘ ⫯*[i]↑f.
 #b #L elim L -L /2 width=1 by frees_atom/
 #L #I #IH *
 [ #H lapply (drops_fwd_isid … H ?) -H // #H destruct
@@ -31,8 +31,8 @@ lemma frees_atom_drops:
 qed.
 
 lemma frees_pair_drops:
-      â\88\80f,K,V. K â\8a¢ ð\9d\90\85+â¦\83Vâ¦\84 ≘ f →
-      ∀i,I,L. ⇩*[i] L ≘ K.ⓑ{I}V → L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i] ↑f.
+      â\88\80f,K,V. K â\8a¢ ð\9d\90\85+â\9dªVâ\9d« ≘ f →
+      ∀i,I,L. ⇩*[i] L ≘ K.ⓑ[I]V → L ⊢ 𝐅+❪#i❫ ≘ ⫯*[i] ↑f.
 #f #K #V #Hf #i elim i -i
 [ #I #L #H lapply (drops_fwd_isid … H ?) -H /2 width=1 by frees_pair/
 | #i #IH #I #L #H elim (drops_inv_succ … H) -H /3 width=2 by frees_lref/
@@ -40,8 +40,8 @@ lemma frees_pair_drops:
 qed.
 
 lemma frees_unit_drops:
-      â\88\80f.  ð\9d\90\88â¦\83fâ¦\84 â\86\92 â\88\80I,K,i,L. â\87©*[i] L â\89\98 K.â\93¤{I} →
-      L â\8a¢ ð\9d\90\85+â¦\83#iâ¦\84 ≘ ⫯*[i] ↑f.
+      â\88\80f.  ð\9d\90\88â\9dªfâ\9d« â\86\92 â\88\80I,K,i,L. â\87©*[i] L â\89\98 K.â\93¤[I] →
+      L â\8a¢ ð\9d\90\85+â\9dª#iâ\9d« ≘ ⫯*[i] ↑f.
 #f #Hf #I #K #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H /2 width=1 by frees_unit/
 | #i #IH #Y #H elim (drops_inv_succ … H) -H
@@ -50,8 +50,8 @@ lemma frees_unit_drops:
 qed.
 
 lemma frees_lref_pushs:
-      â\88\80f,K,j. K â\8a¢ ð\9d\90\85+â¦\83#jâ¦\84 ≘ f →
-      â\88\80i,L. â\87©*[i] L â\89\98 K â\86\92 L â\8a¢ ð\9d\90\85+â¦\83#(i+j)â¦\84 ≘ ⫯*[i] f.
+      â\88\80f,K,j. K â\8a¢ ð\9d\90\85+â\9dª#jâ\9d« ≘ f →
+      â\88\80i,L. â\87©*[i] L â\89\98 K â\86\92 L â\8a¢ ð\9d\90\85+â\9dª#(i+j)â\9d« ≘ ⫯*[i] f.
 #f #K #j #Hf #i elim i -i
 [ #L #H lapply (drops_fwd_isid … H ?) -H //
 | #i #IH #L #H elim (drops_inv_succ … H) -H
@@ -62,10 +62,10 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma frees_inv_lref_drops:
-      â\88\80L,i,f. L â\8a¢ ð\9d\90\85+â¦\83#iâ¦\84 ≘ f →
-      â\88¨â\88¨ â\88\83â\88\83g. â\87©*[â\92»,ð\9d\90\94â\9d´iâ\9dµ] L â\89\98 â\8b\86 & ð\9d\90\88â¦\83gâ¦\84 & f = ⫯*[i] ↑g
-       | â\88\83â\88\83g,I,K,V. K â\8a¢ ð\9d\90\85+â¦\83Vâ¦\84 â\89\98 g & â\87©*[i] L â\89\98 K.â\93\91{I}V & f = ⫯*[i] ↑g
-       | ∃∃g,I,K. ⇩*[i] L ≘ K.ⓤ{I} & 𝐈⦃g⦄ & f = ⫯*[i] ↑g.
+      â\88\80L,i,f. L â\8a¢ ð\9d\90\85+â\9dª#iâ\9d« ≘ f →
+      â\88¨â\88¨ â\88\83â\88\83g. â\87©*[â\92»,ð\9d\90\94â\9d¨iâ\9d©] L â\89\98 â\8b\86 & ð\9d\90\88â\9dªgâ\9d« & f = ⫯*[i] ↑g
+       | â\88\83â\88\83g,I,K,V. K â\8a¢ ð\9d\90\85+â\9dªVâ\9d« â\89\98 g & â\87©*[i] L â\89\98 K.â\93\91[I]V & f = ⫯*[i] ↑g
+       | ∃∃g,I,K. ⇩*[i] L ≘ K.ⓤ[I] & 𝐈❪g❫ & f = ⫯*[i] ↑g.
 #L elim L -L
 [ #i #g | #L #I #IH * [ #g cases I -I [ #I | #I #V ] -IH | #i #g ] ] #H
 [ elim (frees_inv_atom … H) -H #f #Hf #H destruct
@@ -86,9 +86,9 @@ qed-.
 (* Properties with generic slicing for local environments *******************)
 
 lemma frees_lifts:
-      â\88\80b,f1,K,T. K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f1 →
+      â\88\80b,f1,K,T. K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f1 →
       ∀f,L. ⇩*[b,f] L ≘ K → ∀U. ⇧*[f] T ≘ U →
-      â\88\80f2. f ~â\8a\9a f1 â\89\98 f2 â\86\92 L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ f2.
+      â\88\80f2. f ~â\8a\9a f1 â\89\98 f2 â\86\92 L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ f2.
 #b #f1 #K #T #H lapply (frees_fwd_isfin … H) elim H -f1 -K -T
 [ #f1 #K #s #Hf1 #_ #f #L #HLK #U #H2 #f2 #H3
   lapply (coafter_isid_inv_dx … H3 … Hf1) -f1 #Hf2
@@ -144,8 +144,8 @@ lemma frees_lifts:
 qed-.
 
 lemma frees_lifts_SO:
-      â\88\80b,L,K. â\87©*[b,ð\9d\90\94â\9d´1â\9dµ] L ≘ K → ∀T,U. ⇧*[1] T ≘ U →
-      â\88\80f. K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 â\89\98 f â\86\92 L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ ⫯f.
+      â\88\80b,L,K. â\87©*[b,ð\9d\90\94â\9d¨1â\9d©] L ≘ K → ∀T,U. ⇧*[1] T ≘ U →
+      â\88\80f. K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« â\89\98 f â\86\92 L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ ⫯f.
 #b #L #K #HLK #T #U #HTU #f #Hf
 @(frees_lifts b … Hf … HTU) //  (**) (* auto fails *)
 qed.
@@ -153,44 +153,44 @@ qed.
 (* Forward lemmas with generic slicing for local environments ***************)
 
 lemma frees_fwd_coafter:
-      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ f2 →
+      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      â\88\80f1. K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f1 → f ~⊚ f1 ≘ f2.
+      â\88\80f1. K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f1 → f ~⊚ f1 ≘ f2.
 /4 width=11 by frees_lifts, frees_mono, coafter_eq_repl_back0/ qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
 lemma frees_inv_lifts_ex:
-      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ f2 →
+      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      â\88\83â\88\83f1. f ~â\8a\9a f1 â\89\98 f2 & K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f1.
+      â\88\83â\88\83f1. f ~â\8a\9a f1 â\89\98 f2 & K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f1.
 #b #f2 #L #U #Hf2 #f #K #HLK #T elim (frees_total K T)
 /3 width=9 by frees_fwd_coafter, ex2_intro/
 qed-.
 
 lemma frees_inv_lifts_SO:
-      â\88\80b,f,L,U. L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ f →
-      â\88\80K. â\87©*[b,ð\9d\90\94â\9d´1â\9dµ] L ≘ K → ∀T. ⇧*[1] T ≘ U →
-      K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ ⫱f.
+      â\88\80b,f,L,U. L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ f →
+      â\88\80K. â\87©*[b,ð\9d\90\94â\9d¨1â\9d©] L ≘ K → ∀T. ⇧*[1] T ≘ U →
+      K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ ⫱f.
 #b #f #L #U #H #K #HLK #T #HTU elim(frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
 #f1 #Hf #Hf1 elim (coafter_inv_nxx … Hf) -Hf
 /3 width=5 by frees_eq_repl_back, coafter_isid_inv_sn/
 qed-.
 
 lemma frees_inv_lifts:
-      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â¦\83Uâ¦\84 ≘ f2 →
+      â\88\80b,f2,L,U. L â\8a¢ ð\9d\90\85+â\9dªUâ\9d« ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      â\88\80f1. f ~â\8a\9a f1 â\89\98 f2 â\86\92 K â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f1.
+      â\88\80f1. f ~â\8a\9a f1 â\89\98 f2 â\86\92 K â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f1.
 #b #f2 #L #U #H #f #K #HLK #T #HTU #f1 #Hf2 elim (frees_inv_lifts_ex … H … HLK … HTU) -b -L -U
 /3 width=7 by frees_eq_repl_back, coafter_inj/
 qed-.
 
 (* Note: this is used by rex_conf and might be modified *)
 lemma frees_inv_drops_next:
-      â\88\80f1,L1,T1. L1 â\8a¢ ð\9d\90\85+â¦\83T1â¦\84 ≘ f1 →
-      ∀I2,L2,V2,n. ⇩*[n] L1 ≘ L2.ⓑ{I2}V2 →
+      â\88\80f1,L1,T1. L1 â\8a¢ ð\9d\90\85+â\9dªT1â\9d« ≘ f1 →
+      ∀I2,L2,V2,n. ⇩*[n] L1 ≘ L2.ⓑ[I2]V2 →
       ∀g1. ↑g1 = ⫱*[n] f1 →
-      â\88\83â\88\83g2. L2 â\8a¢ ð\9d\90\85+â¦\83V2â¦\84 ≘ g2 & g2 ⊆ g1.
+      â\88\83â\88\83g2. L2 â\8a¢ ð\9d\90\85+â\9dªV2â\9d« ≘ g2 & g2 ⊆ g1.
 #f1 #L1 #T1 #H elim H -f1 -L1 -T1
 [ #f1 #L1 #s #Hf1 #I2 #L2 #V2 #n #_ #g1 #H1 -I2 -L1 -s
   lapply (isid_tls n … Hf1) -Hf1 <H1 -f1 #Hf1