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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "ground_2/notation/functions/liftstar_2.ma".
16 include "ground_2/relocation/rtmap_eq.ma".
18 (* RELOCATION MAP ***********************************************************)
20 rec definition pushs (f:rtmap) (n:nat) on n: rtmap ≝ match n with
21 [ O ⇒ f | S m ⇒ ↑(pushs f m) ].
23 interpretation "pushs (rtmap)" 'LiftStar n f = (pushs f n).
25 (* Basic properties *********************************************************)
27 lemma pushs_O: ∀f. f = ↑*[0] f.
30 lemma pushs_S: ∀f,n. ↑↑*[n] f = ↑*[⫯n] f.
33 lemma pushs_eq_repl: ∀n. eq_repl (λf1,f2. ↑*[n] f1 ≗ ↑*[n] f2).
34 #n elim n -n /3 width=5 by eq_push/
37 (* Advanced properties ******************************************************)
39 lemma pushs_xn: ∀n,f. ↑*[n] ↑f = ↑*[⫯n] f.