update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_isid.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
index d713c1618f048967f1af54cc1e96635a88821738..7fea33f0021f8a370c1d37b89d181a2f08f42e10 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
@@ -18,7 +18,7 @@ include "ground_2/relocation/rtmap_tls.ma".
 (* RELOCATION MAP ***********************************************************)
 
 coinductive isid: predicate rtmap ≝
-| isid_push: â\88\80f,g. isid f â\86\92 â\86\91f = g → isid g
+| isid_push: â\88\80f,g. isid f â\86\92 ⫯f = g → isid g
 .
 
 interpretation "test for identity (rtmap)"
@@ -26,26 +26,26 @@ interpretation "test for identity (rtmap)"
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma isid_inv_gen: â\88\80g. ð\9d\90\88â¦\83gâ¦\84 â\86\92 â\88\83â\88\83f. ð\9d\90\88â¦\83fâ¦\84 & â\86\91f = g.
+lemma isid_inv_gen: â\88\80g. ð\9d\90\88â\9dªgâ\9d« â\86\92 â\88\83â\88\83f. ð\9d\90\88â\9dªfâ\9d« & ⫯f = g.
 #g * -g
 #f #g #Hf * /2 width=3 by ex2_intro/
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma isid_inv_push: â\88\80g. ð\9d\90\88â¦\83gâ¦\84 â\86\92 â\88\80f. â\86\91f = g â\86\92 ð\9d\90\88â¦\83fâ¦\84.
+lemma isid_inv_push: â\88\80g. ð\9d\90\88â\9dªgâ\9d« â\86\92 â\88\80f. ⫯f = g â\86\92 ð\9d\90\88â\9dªfâ\9d«.
 #g #H elim (isid_inv_gen … H) -H
 #f #Hf * -g #g #H >(injective_push … H) -H //
 qed-.
 
-lemma isid_inv_next: â\88\80g. ð\9d\90\88â¦\83gâ¦\84 â\86\92 â\88\80f. ⫯f = g → ⊥.
+lemma isid_inv_next: â\88\80g. ð\9d\90\88â\9dªgâ\9d« â\86\92 â\88\80f. â\86\91f = g → ⊥.
 #g #H elim (isid_inv_gen … H) -H
 #f #Hf * -g #g #H elim (discr_next_push … H)
 qed-.
 
 (* Main inversion lemmas ****************************************************)
 
-corec theorem isid_inv_eq_repl: â\88\80f1,f2. ð\9d\90\88â¦\83f1â¦\84 â\86\92 ð\9d\90\88â¦\83f2â¦\84 â\86\92 f1 â\89\97 f2.
+corec theorem isid_inv_eq_repl: â\88\80f1,f2. ð\9d\90\88â\9dªf1â\9d« â\86\92 ð\9d\90\88â\9dªf2â\9d« â\86\92 f1 â\89¡ f2.
 #f1 #f2 #H1 #H2
 cases (isid_inv_gen … H1) -H1
 cases (isid_inv_gen … H2) -H2
@@ -65,19 +65,31 @@ lemma isid_eq_repl_fwd: eq_repl_fwd … isid.
 
 (* Alternative definition ***************************************************)
 
-corec lemma eq_push_isid: â\88\80f. â\86\91f â\89\97 f â\86\92 ð\9d\90\88â¦\83fâ¦\84.
+corec lemma eq_push_isid: â\88\80f. ⫯f â\89¡ f â\86\92 ð\9d\90\88â\9dªfâ\9d«.
 #f #H cases (eq_inv_px … H) -H /4 width=3 by isid_push, eq_trans/
 qed.
 
-corec lemma eq_push_inv_isid: â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 â\86\91f â\89\97 f.
+corec lemma eq_push_inv_isid: â\88\80f. ð\9d\90\88â\9dªfâ\9d« â\86\92 ⫯f â\89¡ f.
 #f * -f
 #f #g #Hf #Hg @(eq_push … Hg) [2: @eq_push_inv_isid // | skip ]
 @eq_f //
 qed-.
 
+(* Properties with iterated push ********************************************)
+
+lemma isid_pushs: ∀n,f. 𝐈❪f❫ → 𝐈❪⫯*[n]f❫.
+#n elim n -n /3 width=3 by isid_push/
+qed.
+
+(* Inversion lemmas with iterated push **************************************)
+
+lemma isid_inv_pushs: ∀n,g. 𝐈❪⫯*[n]g❫ → 𝐈❪g❫.
+#n elim n -n /3 width=3 by isid_inv_push/
+qed.
+
 (* Properties with tail *****************************************************)
 
-lemma isid_tl: â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 ð\9d\90\88â¦\83⫱fâ¦\84.
+lemma isid_tl: â\88\80f. ð\9d\90\88â\9dªfâ\9d« â\86\92 ð\9d\90\88â\9dªâ«±fâ\9d«.
 #f cases (pn_split f) * #g * -f #H
 [ /2 width=3 by isid_inv_push/
 | elim (isid_inv_next … H) -H //
@@ -86,6 +98,6 @@ qed.
 
 (* Properties with iterated tail ********************************************)
 
-lemma isid_tls: â\88\80n,g. ð\9d\90\88â¦\83gâ¦\84 â\86\92 ð\9d\90\88â¦\83⫱*[n]gâ¦\84.
+lemma isid_tls: â\88\80n,g. ð\9d\90\88â\9dªgâ\9d« â\86\92 ð\9d\90\88â\9dªâ«±*[n]gâ\9d«.
 #n elim n -n /3 width=1 by isid_tl/
 qed.