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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 "trace-okp")
(include-book "../../build/iff")
(include-book "../../build/not")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
;; BOZO find these a home.
(local (in-theory (enable rw.trace-conclusion-formula rw.trace-formula)))
(defthm logic.strip-function-names-of-rw.trace-list-conclusion-formulas-when-all-iffp
(implies (and (all-equalp t (rw.trace-list-iffps x))
(force (rw.trace-listp x)))
(equal (logic.strip-function-names (logic.=lhses (rw.trace-list-conclusion-formulas x)))
(repeat 'iff (len x))))
:hints(("Goal" :in-theory (enable rw.trace-list-conclusion-formulas))))
(defthm logic.strip-lens-of-logic.strip-function-args-of-rw.trace-list-conclusion-formulas
(equal (strip-lens (logic.strip-function-args (logic.=lhses (rw.trace-list-conclusion-formulas x))))
(repeat 2 (len x)))
:hints(("Goal" :in-theory (enable rw.trace-list-conclusion-formulas))))
(deftheorem rw.crewrite-rule-lemma
:derive (v (!= (iff x t) t)
(= (not x) nil))
:proof (@derive
((v (!= x nil) (= (iff x t) nil)) (build.theorem (theorem-iff-t-when-nil)))
((v (!= x nil) (!= (iff x t) t)) (build.disjoined-not-t-from-nil @-))
((v (= x nil) (= (not x) nil)) (build.theorem (theorem-not-when-not-nil)))
((v (= (not x) nil) (!= (iff x t) t)) (build.cut @- @--))
((v (!= (iff x t) t) (= (not x) nil)) (build.commute-or @-)))
:minatbl ((iff . 2)
(not . 1)))
(defderiv rw.crewrite-rule-lemma-bldr
:derive (= (not (? a)) nil)
:from ((proof x (= (iff (? a) t) t)))
:proof (@derive
((v (!= (iff x t) t) (= (not x) nil)) (build.theorem (rw.crewrite-rule-lemma)))
((v (!= (iff (? a) t) t) (= (not (? a)) nil)) (build.instantiation @- (@sigma (x . (? a)))))
((= (iff (? a) t) t) (@given x))
((= (not (? a)) nil) (build.modus-ponens @- @--)))
:minatbl ((iff . 2)
(not . 1)))
(defderiv rw.disjoined-crewrite-rule-lemma-bldr
:derive (v P (= (not (? a)) nil))
:from ((proof x (v P (= (iff (? a) t) t))))
:proof (@derive
((v (!= (iff x t) t) (= (not x) nil)) (build.theorem (rw.crewrite-rule-lemma)))
((v (!= (iff (? a) t) t) (= (not (? a)) nil)) (build.instantiation @- (@sigma (x . (? a)))))
((v P (v (!= (iff (? a) t) t) (= (not (? a)) nil))) (build.expansion (@formula P) @-))
((v P (= (iff (? a) t) t)) (@given x))
((v P (= (not (? a)) nil)) (build.disjoined-modus-ponens @- @--)))
:minatbl ((iff . 2)
(not . 1)))
(defund rw.crewrite-rule-lemma-list-bldr (x)
(declare (xargs :guard (and (logic.appeal-listp x)
(logic.all-atomicp (logic.strip-conclusions x))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions x)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions x))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions x))))))
(if (consp x)
(cons (rw.crewrite-rule-lemma-bldr (car x))
(rw.crewrite-rule-lemma-list-bldr (cdr x)))
nil))
(defobligations rw.crewrite-rule-lemma-list-bldr
(rw.crewrite-rule-lemma-bldr))
(encapsulate
()
(local (in-theory (enable rw.crewrite-rule-lemma-list-bldr)))
(defthm len-of-rw.crewrite-rule-lemma-list-bldr
(equal (len (rw.crewrite-rule-lemma-list-bldr x))
(len x)))
(defthm forcing-logic.appeal-listp-of-rw.crewrite-rule-lemma-list-bldr
(implies (force (and (logic.appeal-listp x)
(logic.all-atomicp (logic.strip-conclusions x))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions x)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions x))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions x)))))
(equal (logic.appeal-listp (rw.crewrite-rule-lemma-list-bldr x))
t)))
(defthm forcing-logic.strip-conclusions-of-rw.crewrite-rule-lemma-list-bldr
(implies (force (and (logic.appeal-listp x)
(logic.all-atomicp (logic.strip-conclusions x))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions x)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions x))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions x)))))
(equal (logic.strip-conclusions (rw.crewrite-rule-lemma-list-bldr x))
(logic.pequal-list (logic.negate-term-list (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(repeat ''nil (len x)))))
:rule-classes ((:rewrite :backchain-limit-lst 0))
:hints(("Goal" :in-theory (enable logic.negate-term))))
(defthm@ forcing-logic.proof-listp-of-rw.crewrite-rule-lemma-list-bldr
(implies (force (and (logic.appeal-listp x)
(logic.all-atomicp (logic.strip-conclusions x))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions x)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions x))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions x)))
;; ---
(logic.proof-listp x axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.crewrite-rule-lemma-list-bldr)
))
(equal (logic.proof-listp (rw.crewrite-rule-lemma-list-bldr x) axioms thms atbl)
t))))
(defund rw.disjoined-crewrite-rule-lemma-list-bldr (p x)
(declare (xargs :guard (and (logic.formulap p)
(logic.appeal-listp x)
(logic.all-disjunctionsp (logic.strip-conclusions x))
(all-equalp p (logic.vlhses (logic.strip-conclusions x)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions x)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions x)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions x)))))))
(if (consp x)
(cons (rw.disjoined-crewrite-rule-lemma-bldr (car x))
(rw.disjoined-crewrite-rule-lemma-list-bldr p (cdr x)))
nil))
(defobligations rw.disjoined-crewrite-rule-lemma-list-bldr
(rw.disjoined-crewrite-rule-lemma-bldr))
(encapsulate
()
(local (in-theory (enable rw.disjoined-crewrite-rule-lemma-list-bldr)))
(defthm len-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(equal (len (rw.disjoined-crewrite-rule-lemma-list-bldr p x))
(len x)))
(defthm forcing-logic.appeal-listp-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(implies (force (and (logic.formulap p)
(logic.appeal-listp x)
(logic.all-disjunctionsp (logic.strip-conclusions x))
(all-equalp p (logic.vlhses (logic.strip-conclusions x)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions x)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions x)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions x))))))
(equal (logic.appeal-listp (rw.disjoined-crewrite-rule-lemma-list-bldr p x))
t)))
(defthm forcing-logic.strip-conclusions-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(implies (force (and (logic.formulap p)
(logic.appeal-listp x)
(logic.all-disjunctionsp (logic.strip-conclusions x))
(all-equalp p (logic.vlhses (logic.strip-conclusions x)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions x)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions x)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions x))))))
(equal (logic.strip-conclusions (rw.disjoined-crewrite-rule-lemma-list-bldr p x))
(logic.por-list (repeat p (len x))
(logic.pequal-list (logic.negate-term-list (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(repeat ''nil (len x))))))
:rule-classes ((:rewrite :backchain-limit-lst 0))
:hints(("Goal" :in-theory (enable logic.negate-term))))
(defthm@ forcing-logic.proof-listp-of-rw.disjoined-crewrite-rule-lemma-list-bldr
(implies (force (and (logic.formulap p)
(logic.appeal-listp x)
(logic.all-disjunctionsp (logic.strip-conclusions x))
(all-equalp p (logic.vlhses (logic.strip-conclusions x)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions x)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions x)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions x))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions x))))
;; ---
(logic.proof-listp x axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.disjoined-crewrite-rule-lemma-list-bldr)
))
(equal (logic.proof-listp (rw.disjoined-crewrite-rule-lemma-list-bldr p x) axioms thms atbl)
t))))
(defund rw.compile-crewrite-rule-trace-lemma1 (rule sigma proofs)
(declare (xargs :guard (and (rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-atomicp (logic.strip-conclusions proofs))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions proofs))))
:verify-guards nil))
;; 1. (not hyp1) != nil v ... v (not hypN) != nil v (equiv lhs rhs) != nil Given (Rule's theorem)
;; 2. (not hyp1/sigma) != nil v ... v (not hypN/sigma) != nil v (equiv lhs/sigma rhs/sigma) != nil Instantiation
;; 3. [[ (iff hyp1/sigma t) = t, ..., (iff hypN/sigma t) = t ]] Givens (Proofs)
;; 4. [[ (not hyp1/sigma) = nil, ..., (not hypN/sigma) = nil ]] CRewrite Rule Lemma List Bldr
;; 5. (equiv lhs/sigma rhs/sigma) != nil Modus Ponens List
(let* ((lhs (rw.rule->lhs rule))
(rhs (rw.rule->rhs rule))
(equiv (rw.rule->equiv rule))
(line-1 (build.theorem (clause.clause-formula (rw.rule-clause rule))))
(line-2 (build.instantiation line-1 sigma))
(line-4 (rw.crewrite-rule-lemma-list-bldr proofs))
(line-5 (build.modus-ponens-list (logic.pnot (logic.pequal (logic.function equiv (list (logic.substitute lhs sigma)
(logic.substitute rhs sigma)))
''nil))
line-4 line-2)))
line-5))
(defobligations rw.compile-crewrite-rule-trace-lemma1
(build.instantiation
rw.crewrite-rule-lemma-list-bldr
build.modus-ponens-list))
(encapsulate
()
(local (in-theory (enable rw.compile-crewrite-rule-trace-lemma1
rw.rule-clause
redefinition-of-logic.term-list-formulas)))
(local (defthm crock
(implies (and (logic.all-negationsp a)
(logic.all-negationsp c)
(force (equal (len a) (len c))) ;; not always true, we force anyway
(force (equal (len b) (len d))) ;; not always true, we force anyway
(force (logic.formula-listp a))
(force (logic.formula-listp b))
(force (logic.formula-listp c))
(force (logic.formula-listp d)))
(equal (equal (logic.disjoin-formulas (app a b))
(logic.disjoin-formulas (app c d)))
(and (equal (list-fix a) (list-fix c))
(equal (list-fix b) (list-fix d)))))))
(local (defthm crock2
(implies (equal (logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma)
(strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (len proofs)
(len (rw.rule->hyps rule))))
:hints(("Goal"
:in-theory (disable len-of-strip-firsts len-of-logic.substitute-list)
:use ((:instance len-of-strip-firsts
(x (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(:instance len-of-logic.substitute-list
(x (rw.hyp-list-terms (rw.rule->hyps rule)))))))))
(defthm logic.appealp-of-rw.compile-crewrite-rule-trace-lemma1
(implies (force (and (rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-atomicp (logic.strip-conclusions proofs))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions proofs)))))
(equal (logic.appealp (rw.compile-crewrite-rule-trace-lemma1 rule sigma proofs))
t)))
(defthm logic.conclusion-of-rw.compile-crewrite-rule-trace-lemma1
(implies (force (and (rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-atomicp (logic.strip-conclusions proofs))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions proofs)))))
(equal (logic.conclusion (rw.compile-crewrite-rule-trace-lemma1 rule sigma proofs))
(logic.pnot
(logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil))))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(local (in-theory (enable rw.rule-env-okp)))
(defthm@ logic.proofp-of-rw.compile-crewrite-rule-trace-lemma1
(implies (force (and (rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-atomicp (logic.strip-conclusions proofs))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions proofs)))
;; ---
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(logic.sigma-atblp sigma atbl)
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.compile-crewrite-rule-trace-lemma1)))
(equal (logic.proofp (rw.compile-crewrite-rule-trace-lemma1 rule sigma proofs) axioms thms atbl)
t)))
(verify-guards rw.compile-crewrite-rule-trace-lemma1))
(defund rw.compile-crewrite-rule-trace-lemma1-okp (x thms atbl)
(declare (xargs :guard (and (logic.appealp x)
(logic.formula-listp thms)
(logic.arity-tablep atbl))))
(let ((method (logic.method x))
(conclusion (logic.conclusion x))
(subproofs (logic.subproofs x))
(extras (logic.extras x)))
(and (equal method 'rw.compile-crewrite-rule-trace-lemma1)
(tuplep 2 extras)
(let ((rule (first extras))
(sigma (second extras)))
(and (rw.rulep rule)
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(logic.sigmap sigma)
(logic.sigma-atblp sigma atbl)
(let ((conclusions (logic.strip-conclusions subproofs)))
(and (logic.all-atomicp conclusions)
(let ((lhses (logic.=lhses conclusions)))
(and (logic.all-functionsp lhses)
(let ((names (logic.strip-function-names lhses))
(args (logic.strip-function-args lhses)))
(and (all-equalp 'iff names)
(all-equalp 2 (strip-lens args))
(equal (strip-firsts args)
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds args))
(all-equalp ''t (logic.=rhses conclusions))
(equal conclusion
(logic.pnot
(logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil))))))))))))))
(defund rw.compile-crewrite-rule-trace-lemma1-high (rule sigma proofs)
(declare (xargs :guard (and (rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-atomicp (logic.strip-conclusions proofs))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions proofs)))))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions proofs))))))
(logic.appeal 'rw.compile-crewrite-rule-trace-lemma1
(logic.pnot (logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil))
(list-fix proofs)
(list rule sigma)))
(encapsulate
()
(local (in-theory (enable rw.compile-crewrite-rule-trace-lemma1-okp)))
(defthm booleanp-of-rw.compile-crewrite-rule-trace-lemma1-okp
(equal (booleanp (rw.compile-crewrite-rule-trace-lemma1-okp x thms atbl))
t)
:hints(("goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm rw.compile-crewrite-rule-trace-lemma1-okp-of-logic.appeal-identity
(equal (rw.compile-crewrite-rule-trace-lemma1-okp (logic.appeal-identity x) thms atbl)
(rw.compile-crewrite-rule-trace-lemma1-okp x thms atbl))
:hints(("goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(local (in-theory (e/d (backtracking-logic.formula-atblp-rules)
(forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free))))
(defthmd lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma1-okp x thms atbl)
(logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl))
(equal (logic.conclusion
(rw.compile-crewrite-rule-trace-lemma1 (first (logic.extras x))
(second (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))
(logic.conclusion x))))
(defthmd@ lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma1-okp x thms atbl)
(logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl)
(@obligations rw.compile-crewrite-rule-trace-lemma1)
(equal (cdr (lookup 'not atbl)) 1))
(equal (logic.proofp
(rw.compile-crewrite-rule-trace-lemma1 (first (logic.extras x))
(second (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl))
axioms thms atbl)
t)))
(defthm@ forcing-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma1-okp x thms atbl)
(force (and (logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl)
(@obligations rw.compile-crewrite-rule-trace-lemma1)
(equal (cdr (lookup 'not atbl)) 1))))
(equal (logic.provablep (logic.conclusion x) axioms thms atbl)
t))
:hints (("Goal"
:in-theory (enable lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp
lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma1-okp)
:use ((:instance forcing-logic.provablep-when-logic.proofp
(x (rw.compile-crewrite-rule-trace-lemma1 (first (logic.extras x))
(second (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))))))))
(defund rw.compile-crewrite-rule-trace-lemma2 (p rule sigma proofs)
(declare (xargs :guard (and (logic.formulap p)
(rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-disjunctionsp (logic.strip-conclusions proofs))
(all-equalp p (logic.vlhses (logic.strip-conclusions proofs)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions proofs)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions proofs)))))
:verify-guards nil))
;; 1. (not hyp1) != nil v ... v (not hypN) != nil v (equiv lhs rhs) != nil Given (Rule's theorem)
;; 2. (not hyp1/sigma) != nil v ... v (not hypN/sigma) != nil v (equiv lhs/sigma rhs/sigma) != nil Instantiation
;; 3. P v (not hyp1/sigma) != nil v ... v (not hypN/sigma) != nil v (equiv lhs/sigma rhs/sigma) != nil Expansion
;; 4. [[ P v (iff hyp1/sigma t) = t, ..., P v (iff hypN/sigma t) = t ]] Givens (Proofs)
;; 5. [[ P v (not hyp1/sigma) = nil, ..., P v (not hypN/sigma) = nil ]] DJ CRewrite Rule Lemma List Bldr
;; 6. P v (equiv lhs/sigma rhs/sigma) != nil DJ Modus Ponens List
(let* ((lhs (rw.rule->lhs rule))
(rhs (rw.rule->rhs rule))
(equiv (rw.rule->equiv rule))
(line-1 (build.theorem (clause.clause-formula (rw.rule-clause rule))))
(line-2 (build.instantiation line-1 sigma))
(line-3 (build.expansion P line-2))
(line-5 (rw.disjoined-crewrite-rule-lemma-list-bldr p proofs))
(line-6 (build.disjoined-modus-ponens-list
(logic.pnot (logic.pequal (logic.function equiv (list (logic.substitute lhs sigma)
(logic.substitute rhs sigma)))
''nil))
line-5 line-3)))
line-6))
(defobligations rw.compile-crewrite-rule-trace-lemma2
(build.expansion
rw.disjoined-crewrite-rule-lemma-list-bldr
build.disjoined-modus-ponens-list))
(encapsulate
()
(local (in-theory (enable rw.compile-crewrite-rule-trace-lemma2
rw.rule-clause
redefinition-of-logic.term-list-formulas)))
(local (defthm crock
(implies (and (logic.all-negationsp a)
(logic.all-negationsp c)
(force (equal (len a) (len c))) ;; not always true, we force anyway
(force (equal (len b) (len d))) ;; not always true, we force anyway
(force (logic.formula-listp a))
(force (logic.formula-listp b))
(force (logic.formula-listp c))
(force (logic.formula-listp d)))
(equal (equal (logic.disjoin-formulas (app a b))
(logic.disjoin-formulas (app c d)))
(and (equal (list-fix a) (list-fix c))
(equal (list-fix b) (list-fix d)))))))
(local (defthm crock2
(implies (equal (logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma)
(strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (len proofs)
(len (rw.rule->hyps rule))))
:hints(("Goal"
:in-theory (disable len-of-strip-firsts len-of-logic.substitute-list)
:use ((:instance len-of-strip-firsts
(x (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(:instance len-of-logic.substitute-list
(x (rw.hyp-list-terms (rw.rule->hyps rule)))))))))
(defthm forcing-logic.appealp-of-rw.compile-crewrite-rule-trace-lemma2
(implies (force (and (logic.formulap p)
(rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-disjunctionsp (logic.strip-conclusions proofs))
(all-equalp p (logic.vlhses (logic.strip-conclusions proofs)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions proofs)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions proofs))))
))
(equal (logic.appealp (rw.compile-crewrite-rule-trace-lemma2 p rule sigma proofs))
t)))
(defthm forcing-logic.conclusion-of-rw.compile-crewrite-rule-trace-lemma2
(implies (force (and (logic.formulap p)
(rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-disjunctionsp (logic.strip-conclusions proofs))
(all-equalp p (logic.vlhses (logic.strip-conclusions proofs)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions proofs)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions proofs))))
))
(equal (logic.conclusion (rw.compile-crewrite-rule-trace-lemma2 p rule sigma proofs))
(logic.por p
(logic.pnot
(logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil)))))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm@ forcing-logic.proofp-of-rw.compile-crewrite-rule-trace-lemma2
(implies (force (and (logic.formulap p)
(rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-disjunctionsp (logic.strip-conclusions proofs))
(all-equalp p (logic.vlhses (logic.strip-conclusions proofs)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions proofs)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions proofs))))
;; ---
(logic.formula-atblp p atbl)
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(logic.sigma-atblp sigma atbl)
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.compile-crewrite-rule-trace-lemma2)
))
(equal (logic.proofp (rw.compile-crewrite-rule-trace-lemma2 p rule sigma proofs) axioms thms atbl)
t))
:hints(("Goal" :in-theory (enable rw.rule-env-okp))))
(verify-guards rw.compile-crewrite-rule-trace-lemma2))
(defund rw.compile-crewrite-rule-trace-lemma2-okp (x thms atbl)
(declare (xargs :guard (and (logic.appealp x)
(logic.formula-listp thms)
(logic.arity-tablep atbl))))
(let ((method (logic.method x))
(conclusion (logic.conclusion x))
(subproofs (logic.subproofs x))
(extras (logic.extras x)))
(and (equal method 'rw.compile-crewrite-rule-trace-lemma2)
(tuplep 3 extras)
(let ((p (first extras))
(rule (second extras))
(sigma (third extras)))
(and (logic.formulap p)
(logic.formula-atblp p atbl)
(rw.rulep rule)
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(logic.sigmap sigma)
(logic.sigma-atblp sigma atbl)
(let ((conclusions (logic.strip-conclusions subproofs)))
(and (logic.all-disjunctionsp conclusions)
(let ((rhses (logic.vrhses conclusions)))
(and (all-equalp p (logic.vlhses conclusions))
(logic.all-atomicp rhses)
(let ((lhses-of-rhses (logic.=lhses rhses)))
(and (logic.all-functionsp lhses-of-rhses)
(all-equalp 'iff (logic.strip-function-names lhses-of-rhses))
(let ((args (logic.strip-function-args lhses-of-rhses)))
(and (all-equalp 2 (strip-lens args))
(equal (strip-firsts args)
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds args))
(all-equalp ''t (logic.=rhses rhses))
(equal conclusion
(logic.por p
(logic.pnot
(logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil)))))))))))))))))
(defund rw.compile-crewrite-rule-trace-lemma2-high (p rule sigma proofs)
(declare (xargs :guard (and (logic.formulap p)
(rw.rulep rule)
(logic.sigmap sigma)
(logic.appeal-listp proofs)
(logic.all-disjunctionsp (logic.strip-conclusions proofs))
(all-equalp p (logic.vlhses (logic.strip-conclusions proofs)))
(logic.all-atomicp (logic.vrhses (logic.strip-conclusions proofs)))
(logic.all-functionsp (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(equal (strip-firsts (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(logic.substitute-list (rw.hyp-list-terms (rw.rule->hyps rule)) sigma))
(all-equalp ''t (strip-seconds (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))))
(all-equalp ''t (logic.=rhses (logic.vrhses (logic.strip-conclusions proofs)))))))
(logic.appeal 'rw.compile-crewrite-rule-trace-lemma2
(logic.por p (logic.pnot (logic.pequal (logic.function (rw.rule->equiv rule)
(list (logic.substitute (rw.rule->lhs rule) sigma)
(logic.substitute (rw.rule->rhs rule) sigma)))
''nil)))
(list-fix proofs)
(list p rule sigma)))
(encapsulate
()
(local (in-theory (enable rw.compile-crewrite-rule-trace-lemma2-okp)))
(defthm booleanp-of-rw.compile-crewrite-rule-trace-lemma2-okp
(equal (booleanp (rw.compile-crewrite-rule-trace-lemma2-okp x thms atbl))
t)
:hints(("goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm rw.compile-crewrite-rule-trace-lemma2-okp-of-logic.appeal-identity
(equal (rw.compile-crewrite-rule-trace-lemma2-okp (logic.appeal-identity x) thms atbl)
(rw.compile-crewrite-rule-trace-lemma2-okp x thms atbl))
:hints(("goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthmd lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma2-okp x thms atbl)
(logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl))
(equal (logic.conclusion
(rw.compile-crewrite-rule-trace-lemma2 (first (logic.extras x))
(second (logic.extras x))
(third (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))
(logic.conclusion x))))
(defthmd@ lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma2-okp x thms atbl)
(logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl)
(@obligations rw.compile-crewrite-rule-trace-lemma2)
(equal (cdr (lookup 'not atbl)) 1))
(equal (logic.proofp
(rw.compile-crewrite-rule-trace-lemma2 (first (logic.extras x))
(second (logic.extras x))
(third (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl))
axioms thms atbl)
t)))
(defthm@ forcing-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
(implies (and (rw.compile-crewrite-rule-trace-lemma2-okp x thms atbl)
(force (and (logic.appealp x)
(logic.provable-listp (logic.strip-conclusions (logic.subproofs x)) axioms thms atbl)
(@obligations rw.compile-crewrite-rule-trace-lemma2)
(equal (cdr (lookup 'not atbl)) 1))))
(equal (logic.provablep (logic.conclusion x) axioms thms atbl)
t))
:hints (("Goal"
:in-theory (enable lemma-1-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp
lemma-2-for-soundness-of-rw.compile-crewrite-rule-trace-lemma2-okp)
:use ((:instance forcing-logic.provablep-when-logic.proofp
(x (rw.compile-crewrite-rule-trace-lemma2 (first (logic.extras x))
(second (logic.extras x))
(third (logic.extras x))
(logic.provable-list-witness
(logic.strip-conclusions (logic.subproofs x))
axioms thms atbl)))))))))
(defund@ rw.compile-crewrite-rule-trace (x proofs)
(declare (xargs :guard (and (rw.tracep x)
(rw.crewrite-rule-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs)
(rw.trace-list-formulas (rw.trace->subtraces x))))
:verify-guards nil))
;; Let the rule be [| rhyp1, ..., rhypN |] ==> (REQUIV rlhs rrhs) = t.
;; Goal: assms v (TEQUIV rlhs/sigma rrhs/sigma) = t
;; Proofs are: assms v (iff rhypi/sigma t) = t
(let* ((hypbox (rw.trace->hypbox x))
(iffp (rw.trace->iffp x))
(extras (rw.trace->extras x))
(rule (first extras))
(sigma (second extras)))
(if (and (not (rw.hypbox->left hypbox))
(not (rw.hypbox->right hypbox)))
(let (;; (REQUIV lhs/sigma rhs/sigma) != nil
(main-proof (rw.compile-crewrite-rule-trace-lemma1 rule sigma proofs)))
(if iffp
(if (equal (rw.rule->equiv rule) 'equal)
;; to cause problems, try (equal (rw.rule->equiv x) 'equal) instead
(build.iff-from-equal (build.equal-t-from-not-nil main-proof))
(build.iff-t-from-not-nil main-proof))
(build.equal-t-from-not-nil main-proof)))
(let* ((f-nhyps (rw.hypbox-formula hypbox))
;; nhyps v (REQUIV lhs/sigma rhs/sigma) != nil
(main-proof (rw.compile-crewrite-rule-trace-lemma2 f-nhyps rule sigma proofs)))
(if iffp
(if (equal (rw.rule->equiv rule) 'equal)
;; to cause problems, try (equal (rw.rule->equiv x) 'equal) instead
(build.disjoined-iff-from-equal (build.disjoined-equal-t-from-not-nil main-proof))
(build.disjoined-iff-t-from-not-nil main-proof))
(build.disjoined-equal-t-from-not-nil main-proof))))))
(defobligations rw.compile-crewrite-rule-trace
(rw.compile-crewrite-rule-trace-lemma1
rw.compile-crewrite-rule-trace-lemma2
build.disjoined-equal-t-from-not-nil
build.disjoined-iff-t-from-not-nil
build.disjoined-iff-from-equal
build.equal-t-from-not-nil
build.iff-t-from-not-nil
build.iff-from-equal))
(encapsulate
()
(local (in-theory (enable rw.compile-crewrite-rule-trace rw.crewrite-rule-tracep)))
(defthmd lemma-1-for-rw.compile-crewrite-rule-trace
(implies (and (equal (rw.trace-list-conclusion-formulas subtraces)
(logic.vrhses (logic.strip-conclusions proofs)))
(all-equalp t (rw.trace-list-iffps subtraces))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(rw.hypbox->right hypbox)
(force (rw.trace-listp subtraces)))
(equal (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(repeat 'iff (len subtraces)))))
(defthmd lemma-2-for-rw.compile-crewrite-rule-trace
(implies (and (equal (rw.trace-list-conclusion-formulas subtraces)
(logic.vrhses (logic.strip-conclusions proofs)))
(all-equalp t (rw.trace-list-iffps subtraces))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(rw.hypbox->left hypbox)
(force (rw.trace-listp subtraces)))
(equal (logic.strip-function-names (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs))))
(repeat 'iff (len subtraces)))))
(defthmd lemma-3-for-rw.compile-crewrite-rule-trace
(implies (and (equal (rw.trace-list-conclusion-formulas subtraces)
(logic.vrhses (logic.strip-conclusions proofs)))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(rw.hypbox->right hypbox)
(force (rw.trace-listp subtraces)))
(equal (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(repeat '2 (len subtraces)))))
(defthmd lemma-4-for-rw.compile-crewrite-rule-trace
(implies (and (equal (rw.trace-list-conclusion-formulas subtraces)
(logic.vrhses (logic.strip-conclusions proofs)))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(rw.hypbox->left hypbox)
(force (rw.trace-listp subtraces)))
(equal (strip-lens (logic.strip-function-args (logic.=lhses (logic.vrhses (logic.strip-conclusions proofs)))))
(repeat '2 (len subtraces)))))
(defthmd lemma-5-for-rw.compile-crewrite-rule-trace
(IMPLIES (AND (EQUAL (RW.TRACE-LIST-CONCLUSION-FORMULAS subtraces)
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(all-equalp t (rw.trace-list-iffps subtraces))
(not (rw.hypbox->left hypbox))
(not (rw.hypbox->right hypbox))
(force (rw.trace-listp subtraces)))
(equal (LOGIC.STRIP-FUNCTION-NAMES (LOGIC.=LHSES (LOGIC.STRIP-CONCLUSIONS PROOFS)))
(repeat 'iff (len subtraces))))
:hints(("Goal"
:in-theory (disable LOGIC.STRIP-FUNCTION-NAMES-OF-RW.TRACE-LIST-CONCLUSION-FORMULAS-WHEN-ALL-IFFP)
:use ((:instance LOGIC.STRIP-FUNCTION-NAMES-OF-RW.TRACE-LIST-CONCLUSION-FORMULAS-WHEN-ALL-IFFP
(x subtraces))))))
(defthmd lemma-6-for-rw.compile-crewrite-rule-trace
(IMPLIES (AND (EQUAL (RW.TRACE-LIST-CONCLUSION-FORMULAS subtraces)
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(all-equalp hypbox (rw.trace-list-hypboxes subtraces))
(not (rw.hypbox->left hypbox))
(not (rw.hypbox->right hypbox))
(force (rw.trace-listp subtraces)))
(equal (STRIP-LENS (LOGIC.STRIP-FUNCTION-ARGS (LOGIC.=LHSES (LOGIC.STRIP-CONCLUSIONS PROOFS))))
(repeat 2 (len subtraces))))
:hints(("Goal"
:in-theory (disable LOGIC.STRIP-LENS-OF-LOGIC.STRIP-FUNCTION-ARGS-OF-RW.TRACE-LIST-CONCLUSION-FORMULAS)
:use ((:instance LOGIC.STRIP-LENS-OF-LOGIC.STRIP-FUNCTION-ARGS-OF-RW.TRACE-LIST-CONCLUSION-FORMULAS
(x subtraces))))))
(local (in-theory (enable lemma-1-for-rw.compile-crewrite-rule-trace
lemma-2-for-rw.compile-crewrite-rule-trace
lemma-3-for-rw.compile-crewrite-rule-trace
lemma-4-for-rw.compile-crewrite-rule-trace
lemma-5-for-rw.compile-crewrite-rule-trace
lemma-6-for-rw.compile-crewrite-rule-trace)))
(defthm rw.compile-crewrite-rule-trace-under-iff
(iff (rw.compile-crewrite-rule-trace x proofs)
t)
:hints(("Goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm forcing-logic.appealp-of-rw.compile-crewrite-rule-trace
(implies (force (and (rw.tracep x)
(rw.crewrite-rule-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs)
(rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.appealp (rw.compile-crewrite-rule-trace x proofs))
t)))
(defthm forcing-logic.conclusion-of-rw.compile-crewrite-rule-trace
(implies (force (and (rw.tracep x)
(rw.crewrite-rule-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs)
(rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.conclusion (rw.compile-crewrite-rule-trace x proofs))
(rw.trace-formula x))))
(defthm@ forcing-logic.proofp-of-rw.compile-crewrite-rule-trace
(implies (force (and (rw.tracep x)
(rw.crewrite-rule-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs)
(rw.trace-list-formulas (rw.trace->subtraces x)))
;; ---
(rw.trace-atblp x atbl)
(rw.crewrite-rule-trace-env-okp x thms atbl)
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(equal (cdr (lookup 'iff atbl)) 2)
(@obligations rw.compile-crewrite-rule-trace)
))
(equal (logic.proofp (rw.compile-crewrite-rule-trace x proofs) axioms thms atbl)
t))
:hints(("Goal" :in-theory (enable rw.crewrite-rule-trace-env-okp))))
(verify-guards rw.compile-crewrite-rule-trace))
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