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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/droppreds_2.ma".
16 include "ground_2/relocation/rtmap_pushs.ma".
17 include "ground_2/relocation/rtmap_tl.ma".
19 (* RELOCATION MAP ***********************************************************)
21 rec definition tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
22 [ O ⇒ f | S m ⇒ ⫱(tls f m) ].
24 interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
26 (* Basic properties *********************************************************)
28 lemma tls_O: ∀f. f = ⫱*[0] f.
31 lemma tls_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[⫯n] f.
34 lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≗ ⫱*[n] f2).
35 #n elim n -n /3 width=1 by tl_eq_repl/
38 (* Advanced properties ******************************************************)
40 lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[⫯n] f.
44 (* Properties with pushs ****************************************************)
46 lemma tls_pushs: ∀n,f. f = ⫱*[n] ↑*[n] f.