(* *)
(**************************************************************************)
-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 â\87\92 f | S m â\87\92 ⫯(nexts f m) ].
+[ O â\87\92 f | S m â\87\92 â\86\91(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: â\88\80n,f1,g2. ⫯*[n] f1 â\89\97 g2 →
- â\88\83â\88\83f2. f1 â\89\97 f2 & ⫯*[n] f2 = g2.
+lemma eq_inv_nexts_sn: â\88\80n,f1,g2. â\86\91*[n] f1 â\89¡ g2 →
+ â\88\83â\88\83f2. f1 â\89¡ f2 & â\86\91*[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: â\88\80n,f2,g1. g1 â\89\97 ⫯*[n] f2 →
- â\88\83â\88\83f1. f1 â\89\97 f2 & ⫯*[n] f1 = g1.
+lemma eq_inv_nexts_dx: â\88\80n,f2,g1. g1 â\89¡ â\86\91*[n] f2 →
+ â\88\83â\88\83f1. f1 â\89¡ f2 & â\86\91*[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
(* Basic properties *********************************************************)
-lemma nexts_O: â\88\80f. f = ⫯*[0] f.
+lemma nexts_O: â\88\80f. f = â\86\91*[0] f.
// qed.
-lemma nexts_S: â\88\80f,n. ⫯⫯*[n] f = ⫯*[⫯n] f.
+lemma nexts_S: â\88\80f,n. â\86\91â\86\91*[n] f = â\86\91*[â\86\91n] f.
// qed.
-lemma nexts_eq_repl: â\88\80n. eq_repl (λf1,f2. ⫯*[n] f1 â\89\97 ⫯*[n] f2).
+lemma nexts_eq_repl: â\88\80n. eq_repl (λf1,f2. â\86\91*[n] f1 â\89¡ â\86\91*[n] f2).
#n elim n -n /3 width=5 by eq_next/
qed.
(* Advanced properties ******************************************************)
-lemma nexts_xn: â\88\80n,f. ⫯*[n] ⫯f = ⫯*[⫯n] f.
+lemma nexts_xn: â\88\80n,f. â\86\91*[n] â\86\91f = â\86\91*[â\86\91n] f.
#n elim n -n //
qed.