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; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "deflist")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
;; (cons-onto-ranges a x)
;;
;; X is a map. We produce a new map whose entries are (key . (a . value))
;; for every (key . value) pair in x.
;; BOZO tail recursive version?
;; BOZO more complete theory?
(defund cons-onto-ranges (a x)
(declare (xargs :guard (mapp x)))
(if (consp x)
(cons (cons (car (car x))
(cons a (cdr (car x))))
(cons-onto-ranges a (cdr x)))
nil))
(defthm cons-onto-ranges-when-not-consp
(implies (not (consp x))
(equal (cons-onto-ranges a x)
nil))
:hints(("Goal" :in-theory (enable cons-onto-ranges))))
(defthm cons-onto-ranges-of-cons
(equal (cons-onto-ranges a (cons b x))
(cons (cons (car b) (cons a (cdr b)))
(cons-onto-ranges a x)))
:hints(("Goal" :in-theory (enable cons-onto-ranges))))
(defthm cons-onto-ranges-of-list-fix
(equal (cons-onto-ranges a (list-fix x))
(cons-onto-ranges a x))
:hints(("Goal" :induct (cdr-induction x))))
(defthm true-listp-of-cons-onto-ranges
(equal (true-listp (cons-onto-ranges a x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm cons-onto-ranges-of-app
(equal (cons-onto-ranges a (app x y))
(app (cons-onto-ranges a x)
(cons-onto-ranges a y)))
:hints(("Goal" :induct (cdr-induction x))))
(defthm mapp-of-cons-onto-ranges
(equal (mapp (cons-onto-ranges a x))
t)
:hints(("Goal" :induct (cdr-induction x))))
(defthm domain-of-cons-onto-ranges
(equal (domain (cons-onto-ranges a x))
(domain x))
:hints(("Goal" :induct (cdr-induction x))))
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