update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / gr_sle.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma
index 6ad077f23c028333f940746355c058313cb55c21..74c15789f00bbc773189e17d68b58a735bfe6bf2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma
@@ -14,7 +14,7 @@
 
 include "ground/relocation/gr_tl.ma".
 
-(* INCLUSION FOR GENERIC RELOCATION MAPS ***********************************************************)
+(* INCLUSION FOR GENERIC RELOCATION MAPS ************************************)
 
 (*** sle *)
 coinductive gr_sle: relation gr_map ≝
@@ -33,7 +33,7 @@ interpretation
   "inclusion (generic relocation maps)"
   'subseteq f1 f2 = (gr_sle f1 f2).
 
-(* Basic properties *********************************************************)
+(* Basic constructions ******************************************************)
 
 (*** sle_refl *)
 corec lemma gr_sle_refl:
@@ -42,7 +42,7 @@ corec lemma gr_sle_refl:
 [ @(gr_sle_push … H H) | @(gr_sle_next … H H) ] -H //
 qed.
 
-(* Basic inversion lemmas ***************************************************)
+(* Basic inversions *********************************************************)
 
 (*** sle_inv_xp *)
 lemma gr_sle_inv_push_dx:
@@ -76,7 +76,7 @@ lemma gr_sle_inv_push_next:
 ]
 qed-.
 
-(* Advanced inversion lemmas ************************************************)
+(* Advanced inversions ******************************************************)
 
 (*** sle_inv_pp *)
 lemma gr_sle_inv_push_bi:
@@ -120,43 +120,43 @@ elim (gr_map_split_tl g1) #H1 #H #f2 #H2
 /3 width=3 by ex2_intro, or_introl, or_intror/
 qed-.
 
-(* Properties with tail *****************************************************)
+(* Constructions with gr_tl *************************************************)
 
 (*** sle_px_tl *)
 lemma gr_sle_push_sn_tl:
-      â\88\80g1,g2. g1 â\8a\86 g2 â\86\92 â\88\80f1. ⫯f1 = g1 â\86\92 f1 â\8a\86 ⫱g2.
+      â\88\80g1,g2. g1 â\8a\86 g2 â\86\92 â\88\80f1. ⫯f1 = g1 â\86\92 f1 â\8a\86 â«°g2.
 #g1 #g2 #H #f1 #H1
 elim (gr_sle_inv_push_sn … H … H1) -H -H1 * //
 qed.
 
 (*** sle_xn_tl *)
 lemma gr_sle_next_dx_tl:
-      â\88\80g1,g2. g1 â\8a\86 g2 â\86\92 â\88\80f2. â\86\91f2 = g2 â\86\92 ⫱g1 ⊆ f2.
+      â\88\80g1,g2. g1 â\8a\86 g2 â\86\92 â\88\80f2. â\86\91f2 = g2 â\86\92 â«°g1 ⊆ f2.
 #g1 #g2 #H #f2 #H2
 elim (gr_sle_inv_next_dx … H … H2) -H -H2 * //
 qed.
 
 (*** sle_tl *)
 lemma gr_sle_tl:
-      â\88\80f1,f2. f1 â\8a\86 f2 â\86\92 ⫱f1 â\8a\86 ⫱f2.
+      â\88\80f1,f2. f1 â\8a\86 f2 â\86\92 â«°f1 â\8a\86 â«°f2.
 #f1 elim (gr_map_split_tl f1) #H1 #f2 #H
 [ lapply (gr_sle_push_sn_tl … H … H1) -H //
 | elim (gr_sle_inv_next_sn … H … H1) -H //
 ]
 qed.
 
-(* Inversion lemmas with tail ***********************************************)
+(* Inversions with gr_tl ****************************************************)
 
 (*** sle_inv_tl_sn *)
 lemma gr_sle_inv_tl_sn:
-      â\88\80f1,f2. ⫱f1 ⊆ f2 → f1 ⊆ ↑f2.
+      â\88\80f1,f2. â«°f1 ⊆ f2 → f1 ⊆ ↑f2.
 #f1 elim (gr_map_split_tl f1) #H #f2 #Hf12
 /2 width=5 by gr_sle_next, gr_sle_weak/
 qed-.
 
 (*** sle_inv_tl_dx *)
 lemma gr_sle_inv_tl_dx:
-      â\88\80f1,f2. f1 â\8a\86 ⫱f2 → ⫯f1 ⊆ f2.
+      â\88\80f1,f2. f1 â\8a\86 â«°f2 → ⫯f1 ⊆ f2.
 #f1 #f2 elim (gr_map_split_tl f2) #H #Hf12
 /2 width=5 by gr_sle_push, gr_sle_weak/
 qed-.