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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 "conditional-eqsubst")
(%interactive)
(%autoadmit tactic.conditional-eqsubst-all-okp)
(%autoadmit tactic.conditional-eqsubst-all-env-okp)
(%autoprove booleanp-of-tactic.conditional-eqsubst-all-okp
(%enable default tactic.conditional-eqsubst-all-okp))
(%autoprove booleanp-of-tactic.conditional-eqsubst-all-env-okp
(%enable default tactic.conditional-eqsubst-all-env-okp))
(defthm forcing-logic.term-list-list-atblp-of-multicons
;; BOZO unlocalize
(implies (force (and (logic.term-atblp a atbl)
(logic.term-list-list-atblp x atbl)))
(equal (logic.term-list-list-atblp (multicons a x) atbl)
t))
:hints(("Goal" :induct (cdr-induction x))))
(%autoprove forcing-logic.term-list-list-atblp-of-multicons
(%cdr-induction x))
(%autoadmit tactic.conditional-eqsubst-all-tac)
(%autoprove forcing-tactic.skeletonp-of-tactic.conditional-eqsubst-all-tac
(%enable default tactic.conditional-eqsubst-all-tac))
(%autoprove forcing-tactic.conditional-eqsubst-all-okp-of-tactic.conditional-eqsubst-all-tac
(%enable default
tactic.conditional-eqsubst-all-tac
tactic.conditional-eqsubst-all-okp))
(%autoprove forcing-tactic.conditional-eqsubst-all-env-okp-of-tactic.conditional-eqsubst-all-tac
(%enable default
tactic.conditional-eqsubst-all-tac
tactic.conditional-eqsubst-all-env-okp))
(%autoadmit tactic.conditional-eqsubst-list-bldr)
(encapsulate
()
(defthmd lemma-1-for-tactic.conditional-eqsubst-list-bldr
(implies (not (consp orig-goals))
(equal (TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR P ORIG-GOALS PROOF1 PROOFS2 PROOFS3 LHS RHS)
nil))
:hints(("Goal" :in-theory (enable TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR))))
(defthmd lemma-2-for-tactic.conditional-eqsubst-list-bldr
(equal (TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR P (cons a ORIG-GOALS) PROOF1 PROOFS2 PROOFS3 LHS RHS)
(CONS (TACTIC.CONDITIONAL-EQSUBST-BLDR P a
PROOF1 (CAR PROOFS2)
(CAR PROOFS3)
LHS RHS)
(TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR P ORIG-GOALS
PROOF1 (CDR PROOFS2)
(CDR PROOFS3)
LHS RHS)))
:hints(("Goal" :in-theory (enable tactic.conditional-eqsubst-list-bldr))))
(%autoprove lemma-1-for-tactic.conditional-eqsubst-list-bldr
(%restrict default TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR (equal orig-goals 'orig-goals)))
(%autoprove lemma-2-for-tactic.conditional-eqsubst-list-bldr
(%restrict default TACTIC.CONDITIONAL-EQSUBST-LIST-BLDR (equal orig-goals '(cons a orig-goals))))
(local (%enable default
lemma-1-for-tactic.conditional-eqsubst-list-bldr
lemma-2-for-tactic.conditional-eqsubst-list-bldr))
(%autoprove forcing-logic.appeal-listp-of-tactic.conditional-eqsubst-list-bldr
(%autoinduct tactic.conditional-eqsubst-list-bldr))
(%autoprove forcing-logic.strip-conclusions-of-tactic.conditional-eqsubst-list-bldr
(%autoinduct tactic.conditional-eqsubst-list-bldr))
(%autoprove forcing-logic.proof-listp-of-tactic.conditional-eqsubst-list-bldr
(%autoinduct tactic.conditional-eqsubst-list-bldr)))
(encapsulate
()
(set-well-founded-relation ord<)
(set-measure-function rank)
(defun firstn-firstn-induct (n x y)
(declare (xargs :measure (nfix n)))
(if (zp n)
nil
(if (not (consp x))
nil
(if (not (consp y))
nil
(firstn-firstn-induct (- n 1) (cdr x) (cdr y)))))))
(defthm lemma-0-for-tactic.conditional-eqsubst-all-compile
;; NOTE: switched order of 1/len x, inc blimit to 1
(implies (not (cdr x))
(equal (equal 1 (len x))
(consp x)))
:rule-classes ((:rewrite :backchain-limit-lst 1)))
(defthm lemma-1-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (logic.conclusion (first proofs))
(logic.disjoin-formulas (logic.term-list-formulas (car goals))))))
(defthm lemma-2-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (logic.strip-conclusions (firstn n proofs))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas (firstn n goals)))))
:hints(("Goal" :in-theory (enable firstn))))
(defthm lemma-3-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (logic.strip-conclusions (restn n proofs))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas (restn n goals)))))
:hints(("Goal" :in-theory (enable restn))))
(defthm lemma-4-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (logic.strip-conclusions (firstn n (cdr proofs)))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas (firstn n (cdr goals)))))))
(defthm lemma-5-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (logic.strip-conclusions (restn n (cdr proofs)))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas (restn n (cdr goals)))))))
(defthm lemma-6-for-tactic.conditional-eqsubst-all-compile
(implies (equal (app a b) x)
(equal (firstn (len a) x)
(list-fix a))))
(defthm lemma-7-for-tactic.conditional-eqsubst-all-compile
(implies (equal (app a b) x)
(equal (restn (len a) x)
(list-fix b))))
(defthm lemma-8-for-tactic.conditional-eqsubst-all-compile
(implies (equal (app a (app b c)) x)
(equal (firstn (len b) (restn (len a) x))
(list-fix b))))
(defthm lemma-9-for-tactic.conditional-eqsubst-all-compile
(implies (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (consp proofs)
(consp goals))))
(defthm lemma-10-for-tactic.conditional-eqsubst-all-compile
(implies (EQUAL (APP (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))) Y)
(CDR (TACTIC.SKELETON->GOALS X)))
(EQUAL (FIRSTN (LEN (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X)))
(CDR (TACTIC.SKELETON->GOALS X)))
(MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X))
(TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X)))))
:hints(("Goal" :use ((:instance lemma-6-for-tactic.conditional-eqsubst-all-compile
(a (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))))
(b y)
(x (CDR (TACTIC.SKELETON->GOALS X))))))))
(defthm lemma-11-for-tactic.conditional-eqsubst-all-compile
(implies (EQUAL (APP (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))) Y)
(CDR (TACTIC.SKELETON->GOALS X)))
(EQUAL (RESTN (LEN (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X)))
(CDR (TACTIC.SKELETON->GOALS X)))
(list-fix Y)))
:hints(("Goal" :use ((:instance lemma-7-for-tactic.conditional-eqsubst-all-compile
(a (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))))
(b y)
(x (CDR (TACTIC.SKELETON->GOALS X))))))))
(defthm lemma-12-for-tactic.conditional-eqsubst-all-compile
(implies (cons-listp x)
(LOGIC.ALL-DISJUNCTIONSP (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (MULTICONS a x)))))
:hints(("Goal" :induct (cdr-induction x))))
(defthm lemma-13-for-tactic.conditional-eqsubst-all-compile
(implies (cons-listp x)
(equal (LOGIC.VLHSES (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (MULTICONS a x))))
(repeat (logic.term-formula a) (len x))))
:hints(("Goal" :induct (cdr-induction x))))
(defthm lemma-14-for-tactic.conditional-eqsubst-all-compile
(implies (cons-listp x)
(equal (LOGIC.VRHSES (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (MULTICONS a x))))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas x))))
:hints(("Goal" :induct (cdr-induction x))))
(%autoprove lemma-0-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-1-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-2-for-tactic.conditional-eqsubst-all-compile
(%autoinduct firstn-firstn-induct n proofs goals)
(%forcingp nil)
(%restrict default firstn (equal n 'n)))
(%autoprove lemma-3-for-tactic.conditional-eqsubst-all-compile
(%autoinduct firstn-firstn-induct n proofs goals)
(%forcingp nil)
(%restrict default restn (equal n 'n)))
(%autoprove lemma-4-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-5-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-6-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-7-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-8-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-9-for-tactic.conditional-eqsubst-all-compile)
(%autoprove lemma-10-for-tactic.conditional-eqsubst-all-compile
(%use (%instance (%thm lemma-6-for-tactic.conditional-eqsubst-all-compile)
(a (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))))
(b y)
(x (CDR (TACTIC.SKELETON->GOALS X))))))
(%autoprove lemma-11-for-tactic.conditional-eqsubst-all-compile
(%use (%instance (%thm lemma-7-for-tactic.conditional-eqsubst-all-compile)
(a (MULTICONS (FIRST (TACTIC.SKELETON->EXTRAS X)) (TACTIC.SKELETON->GOALS (TACTIC.SKELETON->HISTORY X))))
(b y)
(x (CDR (TACTIC.SKELETON->GOALS X))))))
(%autoprove lemma-12-for-tactic.conditional-eqsubst-all-compile
(%cdr-induction x))
(%autoprove lemma-13-for-tactic.conditional-eqsubst-all-compile
(%cdr-induction x))
(%autoprove lemma-14-for-tactic.conditional-eqsubst-all-compile
(%cdr-induction x)
(%forcingp nil))
(%autoadmit tactic.conditional-eqsubst-all-compile)
(local (%enable default
tactic.conditional-eqsubst-all-okp
tactic.conditional-eqsubst-all-env-okp
tactic.conditional-eqsubst-all-compile
logic.term-formula))
(local (%disable default
expensive-arithmetic-rules
expensive-arithmetic-rules-two
unusual-memberp-rules
unusual-subsetp-rules
type-set-like-rules))
(%autoprove forcing-logic.appeal-listp-of-tactic.conditional-eqsubst-all-compile
(%forcingp nil)
(%auto :strategy (cleanup split urewrite))
(%car-cdr-elim proofs)
(%crewrite default first)
(%generalize (car proofs) proof1)
(%generalize (cdr proofs) proofs2)
(%auto :strategy (cleanup split urewrite crewrite dist))
(%disable default
expensive-term/formula-inference
formula-decomposition)
(%forcingp t)
(%waterfall default 40))
(%autoprove forcing-logic.strip-conclusions-of-tactic.conditional-eqsubst-all-compile
(%forcingp nil)
(%auto :strategy (cleanup split urewrite))
(%car-cdr-elim proofs)
(%crewrite default first)
(%generalize (car proofs) proof1)
(%generalize (cdr proofs) proofs2)
(%auto :strategy (cleanup split urewrite crewrite dist))
(%disable default
expensive-term/formula-inference
formula-decomposition)
(%forcingp t)
(%waterfall default 40))
(%autoprove forcing-logic.proof-listp-of-tactic.conditional-eqsubst-all-compile
(%forcingp nil)
(%auto :strategy (cleanup split urewrite))
(%car-cdr-elim proofs)
(%crewrite default first)
(%generalize (car proofs) proof1)
(%generalize (cdr proofs) proofs2)
(%auto :strategy (cleanup split urewrite crewrite dist))
(%disable default
expensive-term/formula-inference
formula-decomposition)
(%forcingp t)
(%waterfall default 40))
(in-theory (disable lemma-0-for-tactic.conditional-eqsubst-all-compile
lemma-1-for-tactic.conditional-eqsubst-all-compile
lemma-2-for-tactic.conditional-eqsubst-all-compile
lemma-3-for-tactic.conditional-eqsubst-all-compile
lemma-4-for-tactic.conditional-eqsubst-all-compile
lemma-5-for-tactic.conditional-eqsubst-all-compile
lemma-6-for-tactic.conditional-eqsubst-all-compile
lemma-7-for-tactic.conditional-eqsubst-all-compile
lemma-8-for-tactic.conditional-eqsubst-all-compile
lemma-9-for-tactic.conditional-eqsubst-all-compile
lemma-10-for-tactic.conditional-eqsubst-all-compile
lemma-11-for-tactic.conditional-eqsubst-all-compile
lemma-12-for-tactic.conditional-eqsubst-all-compile
lemma-13-for-tactic.conditional-eqsubst-all-compile
lemma-14-for-tactic.conditional-eqsubst-all-compile))
(%disable default
lemma-0-for-tactic.conditional-eqsubst-all-compile
lemma-1-for-tactic.conditional-eqsubst-all-compile
lemma-2-for-tactic.conditional-eqsubst-all-compile
lemma-3-for-tactic.conditional-eqsubst-all-compile
lemma-4-for-tactic.conditional-eqsubst-all-compile
lemma-5-for-tactic.conditional-eqsubst-all-compile
lemma-6-for-tactic.conditional-eqsubst-all-compile
lemma-7-for-tactic.conditional-eqsubst-all-compile
lemma-8-for-tactic.conditional-eqsubst-all-compile
lemma-9-for-tactic.conditional-eqsubst-all-compile
lemma-10-for-tactic.conditional-eqsubst-all-compile
lemma-11-for-tactic.conditional-eqsubst-all-compile
lemma-12-for-tactic.conditional-eqsubst-all-compile
lemma-13-for-tactic.conditional-eqsubst-all-compile
lemma-14-for-tactic.conditional-eqsubst-all-compile)
(%ensure-exactly-these-rules-are-missing "../../tactics/conditional-eqsubst-all")
|
