update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor.ma
index 7152502c2016465a176dac7b73194a6d0d634f45..4f2e759e03f5b4b9bf646f9469c800e619ede9ab 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor.ma
@@ -17,7 +17,7 @@ include "ground/xoa/or_3.ma".
 include "ground/xoa/ex_3_2.ma".
 include "ground/relocation/gr_tl.ma".
 
-(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS ***********************************************************)
+(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
 
 (*** sor *)
 coinductive gr_sor: relation3 gr_map gr_map gr_map ≝
@@ -39,7 +39,7 @@ interpretation
   "relational union (generic relocation maps)"
   'RUnion f1 f2 f = (gr_sor f1 f2 f).
 
-(* Basic properties *********************************************************)
+(* Basic constructions ******************************************************)
 
 (*** sor_idem *)
 corec lemma gr_sor_idem:
@@ -58,7 +58,7 @@ corec lemma gr_sor_comm:
 [ @gr_sor_push_bi | @gr_sor_push_next | @gr_sor_next_push | @gr_sor_next_bi ] /2 width=7 by/
 qed-.
 
-(* Basic inversion lemmas ***************************************************)
+(* Basic inversions *********************************************************)
 
 (*** sor_inv_ppx *)
 lemma gr_sor_inv_push_bi:
@@ -112,7 +112,7 @@ try elim (eq_inv_gr_push_next … Hx2) try elim (eq_inv_gr_next_push … Hx2)
 /2 width=3 by ex2_intro/
 qed-.
 
-(* Advanced inversion lemmas ************************************************)
+(* Advanced inversions ******************************************************)
 
 (*** sor_inv_ppn *)
 lemma gr_sor_inv_push_bi_next:
@@ -277,11 +277,11 @@ elim (gr_map_split_tl g1) #H1
 ]
 qed-.
 
-(* Properties with tail *****************************************************)
+(* Constructions with gr_tl *************************************************)
 
 (*** sor_tl *)
 lemma gr_sor_tl:
-      â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ⫱f1 â\8b\93 ⫱f2 â\89\98 ⫱f.
+      â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 â«°f1 â\8b\93 â«°f2 â\89\98 â«°f.
 #f1 cases (gr_map_split_tl f1) #H1
 #f2 cases (gr_map_split_tl f2) #H2
 #f #Hf
@@ -295,8 +295,8 @@ qed.
 (*** sor_xxn_tl *)
 lemma gr_sor_next_tl:
       ∀g1,g2,g. g1 ⋓ g2 ≘ g → ∀f. ↑f = g →
-      (â\88\83â\88\83f1,f2. f1 â\8b\93 f2 â\89\98 f & â\86\91f1 = g1 & ⫱g2 = f2) ∨
-      (â\88\83â\88\83f1,f2. f1 â\8b\93 f2 â\89\98 f & ⫱g1 = f1 & ↑f2 = g2).
+      (â\88\83â\88\83f1,f2. f1 â\8b\93 f2 â\89\98 f & â\86\91f1 = g1 & â«°g2 = f2) ∨
+      (â\88\83â\88\83f1,f2. f1 â\8b\93 f2 â\89\98 f & â«°g1 = f1 & ↑f2 = g2).
 #g1 #g2 #g #H #f #H0 elim (gr_sor_inv_next … H … H0) -H -H0 *
 /3 width=5 by ex3_2_intro, or_introl, or_intror/
 qed-.
@@ -304,7 +304,7 @@ qed-.
 (*** sor_xnx_tl *)
 lemma gr_sor_next_dx_tl:
       ∀g1,g2,g. g1 ⋓ g2 ≘ g → ∀f2. ↑f2 = g2 →
-      â\88\83â\88\83f1,f. f1 â\8b\93 f2 â\89\98 f & ⫱g1 = f1 & ↑f = g.
+      â\88\83â\88\83f1,f. f1 â\8b\93 f2 â\89\98 f & â«°g1 = f1 & ↑f = g.
 #g1 elim (gr_map_split_tl g1) #H1 #g2 #g #H #f2 #H2
 [ elim (gr_sor_inv_push_next … H … H1 H2)
 | elim (gr_sor_inv_next_bi … H … H1 H2)
@@ -315,7 +315,7 @@ qed-.
 (*** sor_nxx_tl *)
 lemma gr_sor_next_sn_tl:
       ∀g1,g2,g. g1 ⋓ g2 ≘ g → ∀f1. ↑f1 = g1 →
-      â\88\83â\88\83f2,f. f1 â\8b\93 f2 â\89\98 f & ⫱g2 = f2 & ↑f = g.
+      â\88\83â\88\83f2,f. f1 â\8b\93 f2 â\89\98 f & â«°g2 = f2 & ↑f = g.
 #g1 #g2 elim (gr_map_split_tl g2) #H2 #g #H #f1 #H1
 [ elim (gr_sor_inv_next_push … H … H1 H2)
 | elim (gr_sor_inv_next_bi … H … H1 H2)
@@ -323,18 +323,18 @@ lemma gr_sor_next_sn_tl:
 /3 width=5 by ex3_2_intro/
 qed-.
 
-(* Inversion lemmas with tail ***********************************************)
+(* Inversions with gr_tl ****************************************************)
 
 (*** sor_inv_tl_sn *)
 lemma gr_sor_inv_tl_sn:
-      â\88\80f1,f2,f. ⫱f1 ⋓ f2 ≘ f → f1 ⋓ ↑f2 ≘ ↑f.
+      â\88\80f1,f2,f. â«°f1 ⋓ f2 ≘ f → f1 ⋓ ↑f2 ≘ ↑f.
 #f1 #f2 #f elim (gr_map_split_tl f1)
 /2 width=7 by gr_sor_push_next, gr_sor_next_bi/
 qed-.
 
 (*** sor_inv_tl_dx *)
 lemma gr_sor_inv_tl_dx:
-      â\88\80f1,f2,f. f1 â\8b\93 ⫱f2 ≘ f → ↑f1 ⋓ f2 ≘ ↑f.
+      â\88\80f1,f2,f. f1 â\8b\93 â«°f2 ≘ f → ↑f1 ⋓ f2 ≘ ↑f.
 #f1 #f2 #f elim (gr_map_split_tl f2)
 /2 width=7 by gr_sor_next_push, gr_sor_next_bi/
 qed-.