1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "ground/notation/functions/oplusleft_3.ma".
16 include "ground/lib/list_append.ma".
18 (* RIGHT CONS FOR LISTS *****************************************************)
22 'OPlusLeft A hd tl = (list_append A hd (list_lcons A tl (list_empty A))).
24 (* Basic constructions ******************************************************)
26 lemma list_cons_comm (A):
30 lemma list_cons_shift (A):
31 ∀a1,l,a2. a1 ⨮{A} l ⨭ a2 = (a1 ⨮ l) ⨭ a2.
34 (* Advanced constructions ***************************************************)
36 (* Note: this is list_append_lcons_dx *)
37 lemma list_append_rcons_sn (A):
38 ∀l1,l2,a. l1 ⨁ (a ⨮ l2) = (l1 ⨭ a) ⨁{A} l2.
41 lemma list_append_rcons_dx (A):
42 ∀l1,l2,a. l1 ⨁ l2 ⨭ a = l1 ⨁{A} (l2 ⨭ a).