X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Frtmap_isfin.ma;h=f79431a17303bd306c160ee66c8e122e7d02f162;hb=cc6fcb70ca4f3cf01205ed722d75a2fdb2aaf779;hp=875378b987c00d56b339ed8ffeb79163b6a15165;hpb=66962864d3703b8f3b44e95d32c03ed50ceee6f1;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
index 875378b98..f79431a17 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
@@ -18,7 +18,7 @@ include "ground_2/relocation/rtmap_fcla.ma".
 (* RELOCATION MAP ***********************************************************)
 
 definition isfin: predicate rtmap ≝
-                  λf. ∃n. 𝐂⦃f⦄ ≡ n.
+                  λf. ∃n. 𝐂⦃f⦄ ≘ n.
 
 interpretation "test for finite colength (rtmap)"
    'IsFinite f = (isfin f).
@@ -26,8 +26,8 @@ interpretation "test for finite colength (rtmap)"
 (* Basic eliminators ********************************************************)
 
 lemma isfin_ind (R:predicate rtmap): (∀f.  𝐈⦃f⦄ → R f) →
-                                     (∀f. 𝐅⦃f⦄ → R f → R (↑f)) →
                                      (∀f. 𝐅⦃f⦄ → R f → R (⫯f)) →
+                                     (∀f. 𝐅⦃f⦄ → R f → R (↑f)) →
                                      ∀f. 𝐅⦃f⦄ → R f.
 #R #IH1 #IH2 #IH3 #f #H elim H -H
 #n #H elim H -f -n /3 width=2 by ex_intro/
@@ -35,11 +35,11 @@ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma isfin_inv_push: ∀g. 𝐅⦃g⦄ → ∀f. ↑f = g → 𝐅⦃f⦄.
+lemma isfin_inv_push: ∀g. 𝐅⦃g⦄ → ∀f. ⫯f = g → 𝐅⦃f⦄.
 #g * /3 width=4 by fcla_inv_px, ex_intro/
 qed-.
 
-lemma isfin_inv_next: ∀g. 𝐅⦃g⦄ → ∀f. ⫯f = g → 𝐅⦃f⦄.
+lemma isfin_inv_next: ∀g. 𝐅⦃g⦄ → ∀f. ↑f = g → 𝐅⦃f⦄.
 #g * #n #H #f #H0 elim (fcla_inv_nx … H … H0) -g
 /2 width=2 by ex_intro/
 qed-.
@@ -56,23 +56,23 @@ lemma isfin_eq_repl_fwd: eq_repl_fwd … isfin.
 lemma isfin_isid: ∀f. 𝐈⦃f⦄ → 𝐅⦃f⦄.
 /3 width=2 by fcla_isid, ex_intro/ qed.
 
-lemma isfin_push: ∀f. 𝐅⦃f⦄ → 𝐅⦃↑f⦄.
+lemma isfin_push: ∀f. 𝐅⦃f⦄ → 𝐅⦃⫯f⦄.
 #f * /3 width=2 by fcla_push, ex_intro/
 qed.
 
-lemma isfin_next: ∀f. 𝐅⦃f⦄ → 𝐅⦃⫯f⦄.
+lemma isfin_next: ∀f. 𝐅⦃f⦄ → 𝐅⦃↑f⦄.
 #f * /3 width=2 by fcla_next, ex_intro/
 qed.
 
 (* Properties with iterated push ********************************************)
 
-lemma isfin_pushs: ∀n,f. 𝐅⦃f⦄ → 𝐅⦃↑*[n]f⦄.
+lemma isfin_pushs: ∀n,f. 𝐅⦃f⦄ → 𝐅⦃⫯*[n]f⦄.
 #n elim n -n /3 width=3 by isfin_push/
 qed.
 
 (* Inversion lemmas with iterated push **************************************)
 
-lemma isfin_inv_pushs: ∀n,g. 𝐅⦃↑*[n]g⦄ → 𝐅⦃g⦄.
+lemma isfin_inv_pushs: ∀n,g. 𝐅⦃⫯*[n]g⦄ → 𝐅⦃g⦄.
 #n elim n -n /3 width=3 by isfin_inv_push/
 qed.