(**************************************************************************)
include "ground_2/notation/functions/droppreds_2.ma".
+include "ground_2/relocation/rtmap_pushs.ma".
include "ground_2/relocation/rtmap_tl.ma".
(* RELOCATION MAP ***********************************************************)
-let rec tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
+rec definition tls (f:rtmap) (n:nat) on n: rtmap ≝ match n with
[ O ⇒ f | S m ⇒ ⫱(tls f m) ].
interpretation "tls (rtmap)" 'DropPreds n f = (tls f n).
(* Basic properties *********************************************************)
-lemma tls_rew_O: ∀f. f = ⫱*[0] f.
+lemma tls_O: ∀f. f = ⫱*[0] f.
// qed.
-lemma tls_rew_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[⫯n] f.
+lemma tls_S: ∀f,n. ⫱ ⫱*[n] f = ⫱*[⫯n] f.
// qed.
lemma tls_eq_repl: ∀n. eq_repl (λf1,f2. ⫱*[n] f1 ≗ ⫱*[n] f2).
#n elim n -n /3 width=1 by tl_eq_repl/
qed.
-(* Advancedd properties *****************************************************)
+(* Advanced properties ******************************************************)
lemma tls_xn: ∀n,f. ⫱*[n] ⫱f = ⫱*[⫯n] f.
#n elim n -n //
qed.
+
+(* Properties with pushs ****************************************************)
+
+lemma tls_pushs: ∀n,f. f = ⫱*[n] ↑*[n] f.
+#n elim n -n //
+#n #IH #f <tls_xn //
+qed.