update in gruound

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / ltc_ctc.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma b/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
index 0f8ddd10789ffefcf2aa2c40909a4e64cce0ff18..e6fcccec6a103586dd91cf17229a75eafc15d268 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
@@ -15,11 +15,11 @@
 include "ground/lib/star.ma".
 include "ground/lib/ltc.ma".
 
-(* LABELLED TRANSITIVE CLOSURE **********************************************)
+(* LABELLED TRANSITIVE CLOSURE FOR RELATIONS ********************************)
 
-alias symbol "subseteq" = "relation inclusion".
+alias symbol "subseteq" = "relation inclusion". (* * alias *)
 
-(* Properties with contextual transitive closure ****************************)
+(* Constructions with ctc ***************************************************)
 
 lemma ltc_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
               left_identity … f i →
@@ -28,13 +28,13 @@ lemma ltc_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
 #b #b2 #_ #Hb2 #IH >(Hf i) -Hf /2 width=3 by ltc_dx/
 qed.
 
-(* Inversion lemmas with contextual transitive closure **********************)
+(* Inversions with ctc ******************************************************)
 
 lemma ltc_inv_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
                   associative … f → annulment_2 … f i →
                   ∀c. ltc … f … (R c) i ⊆ CTC … (λc. R c i) c.
 #C #A #i #f #B #R #H1f #H2f #c #b1 #b2
-@(insert_eq_0 … i) #a #H
+@(insert_eq_1 … i) #a #H
 @(ltc_ind_dx A f B … H) -a -b2 /2 width=1 by inj/ -H1f
 #a1 #a2 #b #b2 #_ #IH #Hb2 #H <H
 elim (H2f … H) -H2f -H #H1 #H2 destruct