matita/matita/contribs/lambdadelta/ground/lib/list_rcons.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "ground/notation/functions/oplusleft_3.ma".
  16 include "ground/lib/list_append.ma".
  17
  18 (* RIGHT CONS FOR LISTS *****************************************************)
  19
  20 interpretation
  21   "right cons (lists)"
  22   'OPlusLeft A hd tl = (list_append A hd (list_lcons A tl (list_empty A))).
  23
  24 (* Basic constructions ******************************************************)
  25
  26 lemma list_cons_comm (A):
  27       ∀a. a ⨮ ⓔ = ⓔ ⨭{A} a.
  28 // qed.
  29
  30 lemma list_cons_shift (A):
  31       ∀a1,l,a2. a1 ⨮{A} l ⨭ a2 = (a1 ⨮ l) ⨭ a2.
  32 // qed.
  33
  34 (* Advanced constructions ***************************************************)
  35
  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.
  39 // qed.
  40
  41 lemma list_append_rcons_dx (A):
  42       ∀l1,l2,a. l1 ⨁ l2 ⨭ a = l1 ⨁{A} (l2 ⨭ a).
  43 // qed.
  44
  45 (* Basic inversions *********************************************************)
  46
  47 lemma eq_inv_list_empty_rcons (A):
  48       ∀l,a. ⓔ = l⨭{A}a → ⊥.
  49 #A #l #a #H
  50 elim (eq_inv_list_empty_append … H) -H #_ #H destruct
  51 qed-.