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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")
(defthmd bust-up-logic.function-args-expensive
(implies (and (ACL2::syntaxp (logic.constantp x))
(consp x))
(equal (equal x (logic.function-args y))
(and (consp (logic.function-args y))
(equal (car x) (car (logic.function-args y)))
(equal (cdr x) (cdr (logic.function-args y))))))
:hints(("Goal" :in-theory (disable FORCING-TRUE-LISTP-OF-LOGIC.FUNCTION-ARGS))))
(defthmd bust-up-cdr-of-logic.function-args-expensive
(implies (and (ACL2::syntaxp (logic.constantp x))
(consp x))
(equal (equal x (cdr (logic.function-args y)))
(and (consp (cdr (logic.function-args y)))
(equal (car x) (car (cdr (logic.function-args y))))
(equal (cdr x) (cdr (cdr (logic.function-args y))))))))
(defthmd bust-up-cdr-of-cdr-of-logic.function-args-expensive
(implies (and (ACL2::syntaxp (logic.constantp x))
(consp x))
(equal (equal x (cdr (cdr (logic.function-args y))))
(and (consp (cdr (cdr (logic.function-args y))))
(equal (car x) (car (cdr (cdr (logic.function-args y)))))
(equal (cdr x) (cdr (cdr (cdr (logic.function-args y)))))))))
(%autoprove bust-up-logic.function-args-expensive (%forcingp nil))
(%autoprove bust-up-cdr-of-logic.function-args-expensive (%forcingp nil))
(%autoprove bust-up-cdr-of-cdr-of-logic.function-args-expensive (%forcingp nil))
;; (DEFTHM CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE-alt
;; (IMPLIES (AND (EQUAL n (lEN X))
;; (SYNTAXP (ACL2::QUOTEP N))
;; (TRUE-LISTP X))
;; (IFF (CDR (CDR X)) (< 2 N))))
;; (%autoprove CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE-alt
;; (%use (%instance (%thm CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE))))
;; (DEFTHM LOGIC.FUNCTION-ARGS-UNDER-IFF-WITH-LEN-FREE-alt
;; (IMPLIES (AND (EQUAL N (LEN (LOGIC.FUNCTION-ARGS TERM)))
;; (SYNTAXP (ACL2::QUOTEP N))
;; (< 0 N))
;; (IFF (LOGIC.FUNCTION-ARGS TERM) T)))
;; (%autoprove LOGIC.FUNCTION-ARGS-UNDER-IFF-WITH-LEN-FREE-alt)
;; (DEFTHM CDR-OF-CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE-alt
;; (IMPLIES (AND (EQUAL n (LEN X))
;; (SYNTAXP (ACL2::QUOTEP N))
;; (TRUE-LISTP X))
;; (IFF (CDR (CDR (CDR X))) (< 3 N))))
;; (%autoprove CDR-OF-CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE-alt
;; (%use (%instance (%thm CDR-OF-CDR-OF-CDR-UNDER-IFF-WHEN-TRUE-LISTP-WITH-LEN-FREE))))
(defthm logic.term-list-atblp-of-cons-gross
(implies (ACL2::syntaxp (logic.constantp x))
(equal (logic.term-list-atblp x atbl)
(if (consp x)
(and (logic.term-atblp (car x) atbl)
(logic.term-list-atblp (cdr x) atbl))
t))))
(%autoprove logic.term-list-atblp-of-cons-gross)
(defthm logic.sigma-atblp-of-cons-gross
(implies (ACL2::syntaxp (logic.constantp x))
(equal (logic.sigma-atblp x atbl)
(if (consp x)
(and (consp (car x))
(logic.variablep (car (car x)))
(logic.term-atblp (cdr (car x)) atbl)
(logic.sigma-atblp (cdr x) atbl))
t))))
(%autoprove logic.sigma-atblp-of-cons-gross)
(defsection logic.substitute-list-of-cons-gross
;; This rule fixes a problem that comes up when we run into terms of the form
;; (logic.substitute-list '(x y) ...). Here, our cons rule does not fire
;; because our patmatch code does not allow it do. We should probably fix
;; our pattern matcher in the long run, but for now we can emulate it in a
;; kind of gross way using a syntactic restriction.
(%prove (%rule logic.substitute-list-of-cons-gross
:hyps (list (%hyp (consp x)))
:lhs (logic.substitute-list x sigma)
:rhs (cons (logic.substitute (car x) sigma)
(logic.substitute-list (cdr x) sigma))
:syntax ((logic.constantp x))))
(%auto)
(%qed)
(%enable default logic.substitute-list-of-cons-gross))
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