X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffrees.ma;h=cdbf5be5aa75aed2d87f727f5a19f6ad0088c7b2;hp=2a72515f43b41c1b7a3fc5646be71e8db39e7733;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/frees.ma b/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
index 2a72515f4..cdbf5be5a 100644
--- a/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/frees.ma
@@ -19,18 +19,18 @@ include "static_2/syntax/lenv.ma".
 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
 
 inductive frees: relation3 lenv term rtmap ≝
-| frees_sort: ∀f,L,s. 𝐈⦃f⦄ → frees L (⋆s) f
-| frees_atom: ∀f,i. 𝐈⦃f⦄ → frees (⋆) (#i) (⫯*[i]↑f)
+| frees_sort: ∀f,L,s. 𝐈❪f❫ → frees L (⋆s) f
+| frees_atom: ∀f,i. 𝐈❪f❫ → frees (⋆) (#i) (⫯*[i]↑f)
 | frees_pair: ∀f,I,L,V. frees L V f →
-              frees (L.ⓑ{I}V) (#0) (↑f)
-| frees_unit: ∀f,I,L. 𝐈⦃f⦄ → frees (L.ⓤ{I}) (#0) (↑f)
+              frees (L.ⓑ[I]V) (#0) (↑f)
+| frees_unit: ∀f,I,L. 𝐈❪f❫ → frees (L.ⓤ[I]) (#0) (↑f)
 | frees_lref: ∀f,I,L,i. frees L (#i) f →
-              frees (L.ⓘ{I}) (#↑i) (⫯f)
-| frees_gref: ∀f,L,l. 𝐈⦃f⦄ → frees L (§l) f
-| frees_bind: ∀f1,f2,f,p,I,L,V,T. frees L V f1 → frees (L.ⓑ{I}V) T f2 →
-              f1 ⋓ ⫱f2 ≘ f → frees L (ⓑ{p,I}V.T) f
+              frees (L.ⓘ[I]) (#↑i) (⫯f)
+| frees_gref: ∀f,L,l. 𝐈❪f❫ → frees L (§l) f
+| frees_bind: ∀f1,f2,f,p,I,L,V,T. frees L V f1 → frees (L.ⓑ[I]V) T f2 →
+              f1 ⋓ ⫱f2 ≘ f → frees L (ⓑ[p,I]V.T) f
 | frees_flat: ∀f1,f2,f,I,L,V,T. frees L V f1 → frees L T f2 →
-              f1 ⋓ f2 ≘ f → frees L (ⓕ{I}V.T) f
+              f1 ⋓ f2 ≘ f → frees L (ⓕ[I]V.T) f
 .
 
 interpretation
@@ -39,7 +39,7 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact frees_inv_sort_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀x. X = ⋆x → 𝐈⦃f⦄.
+fact frees_inv_sort_aux: ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀x. X = ⋆x → 𝐈❪f❫.
 #L #X #f #H elim H -f -L -X //
 [ #f #i #_ #x #H destruct
 | #f #_ #L #V #_ #_ #x #H destruct
@@ -50,12 +50,12 @@ fact frees_inv_sort_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀x. X = ⋆x 
 ]
 qed-.
 
-lemma frees_inv_sort: ∀f,L,s. L ⊢ 𝐅+⦃⋆s⦄ ≘ f → 𝐈⦃f⦄.
+lemma frees_inv_sort: ∀f,L,s. L ⊢ 𝐅+❪⋆s❫ ≘ f → 𝐈❪f❫.
 /2 width=5 by frees_inv_sort_aux/ qed-.
 
 fact frees_inv_atom_aux:
-     ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀i. L = ⋆ → X = #i →
-     ∃∃g. 𝐈⦃g⦄ & f = ⫯*[i]↑g.
+     ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀i. L = ⋆ → X = #i →
+     ∃∃g. 𝐈❪g❫ & f = ⫯*[i]↑g.
 #f #L #X #H elim H -f -L -X
 [ #f #L #s #_ #j #_ #H destruct
 | #f #i #Hf #j #_ #H destruct /2 width=3 by ex2_intro/
@@ -68,12 +68,12 @@ fact frees_inv_atom_aux:
 ]
 qed-.
 
-lemma frees_inv_atom: ∀f,i. ⋆ ⊢ 𝐅+⦃#i⦄ ≘ f → ∃∃g. 𝐈⦃g⦄ & f = ⫯*[i]↑g.
+lemma frees_inv_atom: ∀f,i. ⋆ ⊢ 𝐅+❪#i❫ ≘ f → ∃∃g. 𝐈❪g❫ & f = ⫯*[i]↑g.
 /2 width=5 by frees_inv_atom_aux/ qed-.
 
 fact frees_inv_pair_aux:
-     ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀I,K,V. L = K.ⓑ{I}V → X = #0 →
-     ∃∃g. K ⊢ 𝐅+⦃V⦄ ≘ g & f = ↑g.
+     ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀I,K,V. L = K.ⓑ[I]V → X = #0 →
+     ∃∃g. K ⊢ 𝐅+❪V❫ ≘ g & f = ↑g.
 #f #L #X * -f -L -X
 [ #f #L #s #_ #Z #Y #X #_ #H destruct
 | #f #i #_ #Z #Y #X #H destruct
@@ -86,12 +86,12 @@ fact frees_inv_pair_aux:
 ]
 qed-.
 
-lemma frees_inv_pair: ∀f,I,K,V. K.ⓑ{I}V ⊢ 𝐅+⦃#0⦄ ≘ f → ∃∃g. K ⊢ 𝐅+⦃V⦄ ≘ g & f = ↑g.
+lemma frees_inv_pair: ∀f,I,K,V. K.ⓑ[I]V ⊢ 𝐅+❪#0❫ ≘ f → ∃∃g. K ⊢ 𝐅+❪V❫ ≘ g & f = ↑g.
 /2 width=6 by frees_inv_pair_aux/ qed-.
 
 fact frees_inv_unit_aux:
-     ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀I,K. L = K.ⓤ{I} → X = #0 →
-     ∃∃g. 𝐈⦃g⦄ & f = ↑g.
+     ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀I,K. L = K.ⓤ[I] → X = #0 →
+     ∃∃g. 𝐈❪g❫ & f = ↑g.
 #f #L #X * -f -L -X
 [ #f #L #s #_ #Z #Y #_ #H destruct
 | #f #i #_ #Z #Y #H destruct
@@ -104,12 +104,12 @@ fact frees_inv_unit_aux:
 ]
 qed-.
 
-lemma frees_inv_unit: ∀f,I,K. K.ⓤ{I} ⊢ 𝐅+⦃#0⦄ ≘ f → ∃∃g. 𝐈⦃g⦄ & f = ↑g.
+lemma frees_inv_unit: ∀f,I,K. K.ⓤ[I] ⊢ 𝐅+❪#0❫ ≘ f → ∃∃g. 𝐈❪g❫ & f = ↑g.
 /2 width=7 by frees_inv_unit_aux/ qed-.
 
 fact frees_inv_lref_aux:
-     ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀I,K,j. L = K.ⓘ{I} → X = #(↑j) →
-     ∃∃g. K ⊢ 𝐅+⦃#j⦄ ≘ g & f = ⫯g.
+     ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀I,K,j. L = K.ⓘ[I] → X = #(↑j) →
+     ∃∃g. K ⊢ 𝐅+❪#j❫ ≘ g & f = ⫯g.
 #f #L #X * -f -L -X
 [ #f #L #s #_ #Z #Y #j #_ #H destruct
 | #f #i #_ #Z #Y #j #H destruct
@@ -123,11 +123,11 @@ fact frees_inv_lref_aux:
 qed-.
 
 lemma frees_inv_lref:
-      ∀f,I,K,i. K.ⓘ{I} ⊢ 𝐅+⦃#(↑i)⦄ ≘ f →
-      ∃∃g. K ⊢ 𝐅+⦃#i⦄ ≘ g & f = ⫯g.
+      ∀f,I,K,i. K.ⓘ[I] ⊢ 𝐅+❪#(↑i)❫ ≘ f →
+      ∃∃g. K ⊢ 𝐅+❪#i❫ ≘ g & f = ⫯g.
 /2 width=6 by frees_inv_lref_aux/ qed-.
 
-fact frees_inv_gref_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀x. X = §x → 𝐈⦃f⦄.
+fact frees_inv_gref_aux: ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀x. X = §x → 𝐈❪f❫.
 #f #L #X #H elim H -f -L -X //
 [ #f #i #_ #x #H destruct
 | #f #_ #L #V #_ #_ #x #H destruct
@@ -138,12 +138,12 @@ fact frees_inv_gref_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀x. X = §x 
 ]
 qed-.
 
-lemma frees_inv_gref: ∀f,L,l. L ⊢ 𝐅+⦃§l⦄ ≘ f → 𝐈⦃f⦄.
+lemma frees_inv_gref: ∀f,L,l. L ⊢ 𝐅+❪§l❫ ≘ f → 𝐈❪f❫.
 /2 width=5 by frees_inv_gref_aux/ qed-.
 
 fact frees_inv_bind_aux:
-     ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀p,I,V,T. X = ⓑ{p,I}V.T →
-     ∃∃f1,f2. L ⊢ 𝐅+⦃V⦄ ≘ f1 & L.ⓑ{I}V ⊢ 𝐅+⦃T⦄ ≘ f2 & f1 ⋓ ⫱f2 ≘ f.
+     ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀p,I,V,T. X = ⓑ[p,I]V.T →
+     ∃∃f1,f2. L ⊢ 𝐅+❪V❫ ≘ f1 & L.ⓑ[I]V ⊢ 𝐅+❪T❫ ≘ f2 & f1 ⋓ ⫱f2 ≘ f.
 #f #L #X * -f -L -X
 [ #f #L #s #_ #q #J #W #U #H destruct
 | #f #i #_ #q #J #W #U #H destruct
@@ -157,12 +157,12 @@ fact frees_inv_bind_aux:
 qed-.
 
 lemma frees_inv_bind:
-      ∀f,p,I,L,V,T. L ⊢ 𝐅+⦃ⓑ{p,I}V.T⦄ ≘ f →
-      ∃∃f1,f2. L ⊢ 𝐅+⦃V⦄ ≘ f1 & L.ⓑ{I}V ⊢ 𝐅+⦃T⦄ ≘ f2 & f1 ⋓ ⫱f2 ≘ f.
+      ∀f,p,I,L,V,T. L ⊢ 𝐅+❪ⓑ[p,I]V.T❫ ≘ f →
+      ∃∃f1,f2. L ⊢ 𝐅+❪V❫ ≘ f1 & L.ⓑ[I]V ⊢ 𝐅+❪T❫ ≘ f2 & f1 ⋓ ⫱f2 ≘ f.
 /2 width=4 by frees_inv_bind_aux/ qed-.
 
-fact frees_inv_flat_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀I,V,T. X = ⓕ{I}V.T →
-                         ∃∃f1,f2. L ⊢ 𝐅+⦃V⦄ ≘ f1 & L ⊢ 𝐅+⦃T⦄ ≘ f2 & f1 ⋓ f2 ≘ f.
+fact frees_inv_flat_aux: ∀f,L,X. L ⊢ 𝐅+❪X❫ ≘ f → ∀I,V,T. X = ⓕ[I]V.T →
+                         ∃∃f1,f2. L ⊢ 𝐅+❪V❫ ≘ f1 & L ⊢ 𝐅+❪T❫ ≘ f2 & f1 ⋓ f2 ≘ f.
 #f #L #X * -f -L -X
 [ #f #L #s #_ #J #W #U #H destruct
 | #f #i #_ #J #W #U #H destruct
@@ -176,13 +176,13 @@ fact frees_inv_flat_aux: ∀f,L,X. L ⊢ 𝐅+⦃X⦄ ≘ f → ∀I,V,T. X = 
 qed-.
 
 lemma frees_inv_flat:
-      ∀f,I,L,V,T. L ⊢ 𝐅+⦃ⓕ{I}V.T⦄ ≘ f →
-      ∃∃f1,f2. L ⊢ 𝐅+⦃V⦄ ≘ f1 & L ⊢ 𝐅+⦃T⦄ ≘ f2 & f1 ⋓ f2 ≘ f.
+      ∀f,I,L,V,T. L ⊢ 𝐅+❪ⓕ[I]V.T❫ ≘ f →
+      ∃∃f1,f2. L ⊢ 𝐅+❪V❫ ≘ f1 & L ⊢ 𝐅+❪T❫ ≘ f2 & f1 ⋓ f2 ≘ f.
 /2 width=4 by frees_inv_flat_aux/ qed-.
 
 (* Basic properties ********************************************************)
 
-lemma frees_eq_repl_back: ∀L,T. eq_repl_back … (λf. L ⊢ 𝐅+⦃T⦄ ≘ f).
+lemma frees_eq_repl_back: ∀L,T. eq_repl_back … (λf. L ⊢ 𝐅+❪T❫ ≘ f).
 #L #T #f1 #H elim H -f1 -L -T
 [ /3 width=3 by frees_sort, isid_eq_repl_back/
 | #f1 #i #Hf1 #g2 #H
@@ -203,11 +203,11 @@ lemma frees_eq_repl_back: ∀L,T. eq_repl_back … (λf. L ⊢ 𝐅+⦃T⦄ ≘
 ]
 qed-.
 
-lemma frees_eq_repl_fwd: ∀L,T. eq_repl_fwd … (λf. L ⊢ 𝐅+⦃T⦄ ≘ f).
+lemma frees_eq_repl_fwd: ∀L,T. eq_repl_fwd … (λf. L ⊢ 𝐅+❪T❫ ≘ f).
 #L #T @eq_repl_sym /2 width=3 by frees_eq_repl_back/
 qed-.
 
-lemma frees_lref_push: ∀f,i. ⋆ ⊢ 𝐅+⦃#i⦄ ≘ f → ⋆ ⊢ 𝐅+⦃#↑i⦄ ≘ ⫯f.
+lemma frees_lref_push: ∀f,i. ⋆ ⊢ 𝐅+❪#i❫ ≘ f → ⋆ ⊢ 𝐅+❪#↑i❫ ≘ ⫯f.
 #f #i #H
 elim (frees_inv_atom … H) -H #g #Hg #H destruct
 /2 width=1 by frees_atom/
@@ -215,7 +215,7 @@ qed.
 
 (* Forward lemmas with test for finite colength *****************************)
 
-lemma frees_fwd_isfin: ∀f,L,T. L ⊢ 𝐅+⦃T⦄ ≘ f → 𝐅⦃f⦄.
+lemma frees_fwd_isfin: ∀f,L,T. L ⊢ 𝐅+❪T❫ ≘ f → 𝐅❪f❫.
 #f #L #T #H elim H -f -L -T
 /4 width=5 by sor_isfin, isfin_isid, isfin_tl, isfin_pushs, isfin_push, isfin_next/
 qed-.