X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffrees_drops.ma;h=37c629351f1c30b64f19adb8ee78124871942f2a;hp=bc5a7056babb2ba2b28e75aa6627e699554963f0;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

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 bc5a7056b..37c629351 100644
--- 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:
-      ∀b,L,i. ⇩*[b,𝐔❴i❵] L ≘ ⋆ →
-      ∀f. 𝐈⦃f⦄ → L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i]↑f.
+      ∀b,L,i. ⇩*[b,𝐔❨i❩] L ≘ ⋆ →
+      ∀f. 𝐈❪f❫ → L ⊢ 𝐅+❪#i❫ ≘ ⫯*[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:
-      ∀f,K,V. K ⊢ 𝐅+⦃V⦄ ≘ f →
-      ∀i,I,L. ⇩*[i] L ≘ K.ⓑ{I}V → L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i] ↑f.
+      ∀f,K,V. K ⊢ 𝐅+❪V❫ ≘ 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:
-      ∀f.  𝐈⦃f⦄ → ∀I,K,i,L. ⇩*[i] L ≘ K.ⓤ{I} →
-      L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i] ↑f.
+      ∀f.  𝐈❪f❫ → ∀I,K,i,L. ⇩*[i] L ≘ K.ⓤ[I] →
+      L ⊢ 𝐅+❪#i❫ ≘ ⫯*[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:
-      ∀f,K,j. K ⊢ 𝐅+⦃#j⦄ ≘ f →
-      ∀i,L. ⇩*[i] L ≘ K → L ⊢ 𝐅+⦃#(i+j)⦄ ≘ ⫯*[i] f.
+      ∀f,K,j. K ⊢ 𝐅+❪#j❫ ≘ f →
+      ∀i,L. ⇩*[i] L ≘ K → L ⊢ 𝐅+❪#(i+j)❫ ≘ ⫯*[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:
-      ∀L,i,f. L ⊢ 𝐅+⦃#i⦄ ≘ f →
-      ∨∨ ∃∃g. ⇩*[Ⓕ,𝐔❴i❵] L ≘ ⋆ & 𝐈⦃g⦄ & f = ⫯*[i] ↑g
-       | ∃∃g,I,K,V. K ⊢ 𝐅+⦃V⦄ ≘ g & ⇩*[i] L ≘ K.ⓑ{I}V & f = ⫯*[i] ↑g
-       | ∃∃g,I,K. ⇩*[i] L ≘ K.ⓤ{I} & 𝐈⦃g⦄ & f = ⫯*[i] ↑g.
+      ∀L,i,f. L ⊢ 𝐅+❪#i❫ ≘ f →
+      ∨∨ ∃∃g. ⇩*[Ⓕ,𝐔❨i❩] L ≘ ⋆ & 𝐈❪g❫ & f = ⫯*[i] ↑g
+       | ∃∃g,I,K,V. K ⊢ 𝐅+❪V❫ ≘ g & ⇩*[i] L ≘ K.ⓑ[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:
-      ∀b,f1,K,T. K ⊢ 𝐅+⦃T⦄ ≘ f1 →
+      ∀b,f1,K,T. K ⊢ 𝐅+❪T❫ ≘ f1 →
       ∀f,L. ⇩*[b,f] L ≘ K → ∀U. ⇧*[f] T ≘ U →
-      ∀f2. f ~⊚ f1 ≘ f2 → L ⊢ 𝐅+⦃U⦄ ≘ f2.
+      ∀f2. f ~⊚ f1 ≘ f2 → L ⊢ 𝐅+❪U❫ ≘ 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:
-      ∀b,L,K. ⇩*[b,𝐔❴1❵] L ≘ K → ∀T,U. ⇧*[1] T ≘ U →
-      ∀f. K ⊢ 𝐅+⦃T⦄ ≘ f → L ⊢ 𝐅+⦃U⦄ ≘ ⫯f.
+      ∀b,L,K. ⇩*[b,𝐔❨1❩] L ≘ K → ∀T,U. ⇧*[1] T ≘ U →
+      ∀f. K ⊢ 𝐅+❪T❫ ≘ f → L ⊢ 𝐅+❪U❫ ≘ ⫯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:
-      ∀b,f2,L,U. L ⊢ 𝐅+⦃U⦄ ≘ f2 →
+      ∀b,f2,L,U. L ⊢ 𝐅+❪U❫ ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      ∀f1. K ⊢ 𝐅+⦃T⦄ ≘ f1 → f ~⊚ f1 ≘ f2.
+      ∀f1. K ⊢ 𝐅+❪T❫ ≘ 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:
-      ∀b,f2,L,U. L ⊢ 𝐅+⦃U⦄ ≘ f2 →
+      ∀b,f2,L,U. L ⊢ 𝐅+❪U❫ ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      ∃∃f1. f ~⊚ f1 ≘ f2 & K ⊢ 𝐅+⦃T⦄ ≘ f1.
+      ∃∃f1. f ~⊚ f1 ≘ f2 & K ⊢ 𝐅+❪T❫ ≘ 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:
-      ∀b,f,L,U. L ⊢ 𝐅+⦃U⦄ ≘ f →
-      ∀K. ⇩*[b,𝐔❴1❵] L ≘ K → ∀T. ⇧*[1] T ≘ U →
-      K ⊢ 𝐅+⦃T⦄ ≘ ⫱f.
+      ∀b,f,L,U. L ⊢ 𝐅+❪U❫ ≘ f →
+      ∀K. ⇩*[b,𝐔❨1❩] L ≘ K → ∀T. ⇧*[1] T ≘ U →
+      K ⊢ 𝐅+❪T❫ ≘ ⫱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:
-      ∀b,f2,L,U. L ⊢ 𝐅+⦃U⦄ ≘ f2 →
+      ∀b,f2,L,U. L ⊢ 𝐅+❪U❫ ≘ f2 →
       ∀f,K. ⇩*[b,f] L ≘ K → ∀T. ⇧*[f] T ≘ U →
-      ∀f1. f ~⊚ f1 ≘ f2 → K ⊢ 𝐅+⦃T⦄ ≘ f1.
+      ∀f1. f ~⊚ f1 ≘ f2 → K ⊢ 𝐅+❪T❫ ≘ 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:
-      ∀f1,L1,T1. L1 ⊢ 𝐅+⦃T1⦄ ≘ f1 →
-      ∀I2,L2,V2,n. ⇩*[n] L1 ≘ L2.ⓑ{I2}V2 →
+      ∀f1,L1,T1. L1 ⊢ 𝐅+❪T1❫ ≘ f1 →
+      ∀I2,L2,V2,n. ⇩*[n] L1 ≘ L2.ⓑ[I2]V2 →
       ∀g1. ↑g1 = ⫱*[n] f1 →
-      ∃∃g2. L2 ⊢ 𝐅+⦃V2⦄ ≘ g2 & g2 ⊆ g1.
+      ∃∃g2. L2 ⊢ 𝐅+❪V2❫ ≘ 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