update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls.ma
index f297468f9bc80fb0c2be569210e3071e70d2d9a7..0402e2929db2fca38b107edd0af2f52e77037bcd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls.ma
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls.ma
@@ -16,14 +16,14 @@ include "ground/relocation/gr_tls.ma".
 include "ground/relocation/gr_nat.ma".
 include "ground/relocation/gr_coafter.ma".
 
-(* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+(* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
 
-(* Properties with nat and iterated tail ********************************************)
+(* Constructions with gr_nat and gr_tls *************************************)
 
 (*** coafter_tls *)
 lemma gr_coafter_tls_bi_tls (n2) (n1):
       ∀f1,f2,f. @↑❪n1, f1❫ ≘ n2 →
-      f1 ~â\8a\9a f2 â\89\98 f â\86\92 ⫱*[n2]f1 ~â\8a\9a ⫱*[n1]f2 â\89\98 ⫱*[n2]f.
+      f1 ~â\8a\9a f2 â\89\98 f â\86\92 â«°*[n2]f1 ~â\8a\9a â«°*[n1]f2 â\89\98 â«°*[n2]f.
 #n2 @(nat_ind_succ … n2) -n2 [ #n1 | #n2 #IH * [| #n1 ] ] #f1 #f2 #f #Hf1 #Hf
 [ elim (gr_nat_inv_zero_dx … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1 destruct //
 | elim (gr_nat_inv_zero_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
@@ -41,5 +41,5 @@ qed.
 (*** coafter_tls_O *)
 lemma gr_coafter_tls_sn_tls:
       ∀n,f1,f2,f. @↑❪𝟎, f1❫ ≘ n →
-      f1 ~â\8a\9a f2 â\89\98 f â\86\92 ⫱*[n]f1 ~â\8a\9a f2 â\89\98 ⫱*[n]f.
+      f1 ~â\8a\9a f2 â\89\98 f â\86\92 â«°*[n]f1 ~â\8a\9a f2 â\89\98 â«°*[n]f.
 /2 width=1 by gr_coafter_tls_bi_tls/ qed.