X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Frtmap_nexts.ma;h=2de10f889471410377fcdef049ad5d179d77823a;hb=1fd63df4c77f5c24024769432ea8492748b4ac79;hp=91e916d9360c416a2fe731c4b0de2cc8fe58066f;hpb=66962864d3703b8f3b44e95d32c03ed50ceee6f1;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_nexts.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_nexts.ma
index 91e916d93..2de10f889 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_nexts.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_nexts.ma
@@ -12,28 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/notation/functions/successorstar_2.ma".
+include "ground_2/notation/functions/uparrowstar_2.ma".
 include "ground_2/relocation/rtmap_eq.ma".
 
 (* RELOCATION MAP ***********************************************************)
 
 rec definition nexts (f:rtmap) (n:nat) on n: rtmap ≝ match n with
-[ O ⇒ f | S m ⇒ ⫯(nexts f m) ].
+[ O ⇒ f | S m ⇒ ↑(nexts f m) ].
 
-interpretation "nexts (rtmap)" 'SuccessorStar n f = (nexts f n).
+interpretation "nexts (rtmap)" 'UpArrowStar n f = (nexts f n).
 
 (* Basic_inversion lemmas *****************************************************)
 
-lemma eq_inv_nexts_sn: ∀n,f1,g2. ⫯*[n] f1 ≗ g2 →
-                       ∃∃f2. f1 ≗ f2 & ⫯*[n] f2 = g2.
+lemma eq_inv_nexts_sn: ∀n,f1,g2. ↑*[n] f1 ≡ g2 →
+                       ∃∃f2. f1 ≡ f2 & ↑*[n] f2 = g2.
 #n elim n -n /2 width=3 by ex2_intro/
 #n #IH #f1 #g2 #H elim (eq_inv_nx … H) -H [|*: // ]
 #f0 #Hf10 #H1 elim (IH … Hf10) -IH -Hf10 #f2 #Hf12 #H2 destruct
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma eq_inv_nexts_dx: ∀n,f2,g1. g1 ≗ ⫯*[n] f2 →
-                       ∃∃f1. f1 ≗ f2 & ⫯*[n] f1 = g1.
+lemma eq_inv_nexts_dx: ∀n,f2,g1. g1 ≡ ↑*[n] f2 →
+                       ∃∃f1. f1 ≡ f2 & ↑*[n] f1 = g1.
 #n elim n -n /2 width=3 by ex2_intro/
 #n #IH #f2 #g1 #H elim (eq_inv_xn … H) -H [|*: // ]
 #f0 #Hf02 #H1 elim (IH … Hf02) -IH -Hf02 #f1 #Hf12 #H2 destruct
@@ -42,18 +42,18 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma nexts_O: ∀f. f = ⫯*[0] f.
+lemma nexts_O: ∀f. f = ↑*[0] f.
 // qed.
 
-lemma nexts_S: ∀f,n. ⫯⫯*[n] f = ⫯*[⫯n] f.
+lemma nexts_S: ∀f,n. ↑↑*[n] f = ↑*[↑n] f.
 // qed.
 
-lemma nexts_eq_repl: ∀n. eq_repl (λf1,f2. ⫯*[n] f1 ≗ ⫯*[n] f2).
+lemma nexts_eq_repl: ∀n. eq_repl (λf1,f2. ↑*[n] f1 ≡ ↑*[n] f2).
 #n elim n -n /3 width=5 by eq_next/
 qed.
 
 (* Advanced properties ******************************************************)
 
-lemma nexts_xn: ∀n,f. ⫯*[n] ⫯f = ⫯*[⫯n] f.
+lemma nexts_xn: ∀n,f. ↑*[n] ↑f = ↑*[↑n] f.
 #n elim n -n //
 qed.