/usr/share/acl2-6.3/books/data-structures/no-duplicates.lisp is in acl2-books-source 6.3-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 | ; no-duplicates.lisp: Reasoning about no-duplicatesp-equal and
; intersectp-equal. Name-compatible with list-theory.lisp and set-theory.lisp.
; Copyright (C) 2010 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version. This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
; more details. You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Sol Swords <sswords@centtech.com>
(in-package "ACL2")
(defthm associativity-of-append
;; Renamed by Jared for compatibility with data-structures/list-defthms
(equal (append (append a b) c)
(append a (append b c))))
(defthm member-equal-append
(iff (member-equal x (append a b))
(or (member-equal x a)
(member-equal x b))))
;; Note: inesrting double-rewrites here because A and B are now in a
;; set-equivalence context within intersectp-equal, whereas they weren't
;; within no-duplicatesp-equal.
(defthm no-duplicatesp-equal-append-iff
(iff (no-duplicatesp-equal (append a b))
(and (no-duplicatesp-equal a)
(no-duplicatesp-equal b)
(not (intersectp-equal (double-rewrite a)
(double-rewrite b))))))
(defthm intersectp-equal-append1
(equal (intersectp-equal (append a b) c)
(or (intersectp-equal a c)
(intersectp-equal b c))))
(defthm intersectp-equal-cons-second
(iff (intersectp-equal a (cons c b))
(or (member-equal c a)
(intersectp-equal a b))))
(defthm intersectp-equal-non-cons-1
(implies (not (consp a))
(not (intersectp-equal a b))))
(defthm intersectp-equal-non-cons
(implies (not (consp b))
(not (intersectp-equal a b))))
(defthm intersectp-equal-append2
(equal (intersectp-equal c (append a b))
(or (intersectp-equal c a)
(intersectp-equal c b))))
(defthm intersectp-equal-commute
(iff (intersectp-equal a b)
(intersectp-equal b a)))
; [Removed by Matt K. to handle changes to member, assoc, etc. after ACL2 4.2.]
; (defthm member-is-member-equal
; (equal (member x y) (member-equal x y)))
; [Removed by Matt K. to handle changes to member, assoc, etc. after ACL2 4.2.]
; (defthm no-duplicatesp-is-no-duplicatesp-equal
; (equal (no-duplicatesp x)
; (no-duplicatesp-equal x)))
(defthm no-duplicatesp-equal-non-cons
(implies (not (consp x))
(no-duplicatesp-equal x)))
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