X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Frtmap_isid.ma;h=4fa424d494f1f535e3eedbba964023dbb8f046f5;hb=397413c4196f84c81d61ba7dd79b54ab1c428ebb;hp=65e111bbf9d3e209bbb6516965ff215c934dd339;hpb=24ba1bb3f67505d3e384747ff90d26d3996bd3f5;p=helm.git

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 65e111bbf..4fa424d49 100644
--- 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: ∀f,g. isid f → ↑f = g → isid g
+| isid_push: ∀f,g. isid f → ⫯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: ∀g. 𝐈⦃g⦄ → ∃∃f. 𝐈⦃f⦄ & ↑f = g.
+lemma isid_inv_gen: ∀g. 𝐈⦃g⦄ → ∃∃f. 𝐈⦃f⦄ & ⫯f = g.
 #g * -g
 #f #g #Hf * /2 width=3 by ex2_intro/
 qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma isid_inv_push: ∀g. 𝐈⦃g⦄ → ∀f. ↑f = g → 𝐈⦃f⦄.
+lemma isid_inv_push: ∀g. 𝐈⦃g⦄ → ∀f. ⫯f = g → 𝐈⦃f⦄.
 #g #H elim (isid_inv_gen … H) -H
 #f #Hf * -g #g #H >(injective_push … H) -H //
 qed-.
 
-lemma isid_inv_next: ∀g. 𝐈⦃g⦄ → ∀f. ⫯f = g → ⊥.
+lemma isid_inv_next: ∀g. 𝐈⦃g⦄ → ∀f. ↑f = 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: ∀f1,f2. 𝐈⦃f1⦄ → 𝐈⦃f2⦄ → f1 ≗ f2.
+corec theorem isid_inv_eq_repl: ∀f1,f2. 𝐈⦃f1⦄ → 𝐈⦃f2⦄ → f1 ≡ f2.
 #f1 #f2 #H1 #H2
 cases (isid_inv_gen … H1) -H1
 cases (isid_inv_gen … H2) -H2
@@ -65,11 +65,11 @@ lemma isid_eq_repl_fwd: eq_repl_fwd … isid.
 
 (* Alternative definition ***************************************************)
 
-corec lemma eq_push_isid: ∀f. ↑f ≗ f → 𝐈⦃f⦄.
+corec lemma eq_push_isid: ∀f. ⫯f ≡ f → 𝐈⦃f⦄.
 #f #H cases (eq_inv_px … H) -H /4 width=3 by isid_push, eq_trans/
 qed.
 
-corec lemma eq_push_inv_isid: ∀f. 𝐈⦃f⦄ → ↑f ≗ f.
+corec lemma eq_push_inv_isid: ∀f. 𝐈⦃f⦄ → ⫯f ≡ f.
 #f * -f
 #f #g #Hf #Hg @(eq_push … Hg) [2: @eq_push_inv_isid // | skip ]
 @eq_f //
@@ -77,13 +77,13 @@ qed-.
 
 (* Properties with iterated push ********************************************)
 
-lemma isid_pushs: ∀n,f. 𝐈⦃f⦄ → 𝐈⦃↑*[n]f⦄.
+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⦄.
+lemma isid_inv_pushs: ∀n,g. 𝐈⦃⫯*[n]g⦄ → 𝐈⦃g⦄.
 #n elim n -n /3 width=3 by isid_inv_push/
 qed.