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|
; RP-REWRITER
; Note: The license below is based on the template at:
; http://opensource.org/licenses/BSD-3-Clause
; Copyright (C) 2019, Regents of the University of Texas
; All rights reserved.
; Copyright (C) 2022 Intel Corporation
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are
; met:
; o Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; o Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
; o Neither the name of the copyright holders nor the names of its
; contributors may be used to endorse or promote products derived
; from this software without specific prior written permission.
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
; HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
; Original Author(s):
; Mertcan Temel <mert@utexas.edu>
(in-package "RP")
(include-Book "proof-functions")
(include-Book "eval-functions-lemmas")
(local (include-book "aux-function-lemmas"))
(local
(in-theory (enable falist-consistent)))
(defthm eval-and-all-append
(equal (eval-and-all (append x y) a)
(and (eval-and-all x a)
(eval-and-all y a)))
:hints (("Goal"
:in-theory (e/d (eval-and-all
append) ()))))
#|(encapsulate
nil
(local
(defthm flag-for-not-include-rp-of-beta-reduce-term
(implies (and (not (include-fnc-subterms vals 'rp))
#|(symbol-listp keys)||#
(if arg
(not (include-fnc-subterms term 'rp))
(not (include-fnc term 'rp))))
(if arg
(not (include-fnc-subterms (acl2::beta-reduce-term arg term keys vals)
'rp))
(not (include-fnc (acl2::beta-reduce-term arg term keys vals)
'rp))))))
(defthm not-include-rp-of-beta-reduce-term-arg=nil
(implies (and (not (include-fnc-subterms vals 'rp))
#|(symbol-listp keys)||#
(not (include-fnc term 'rp)))
(not (include-fnc (acl2::beta-reduce-term nil term keys vals)
'rp)))
:hints (("Goal"
:use ((:instance flag-for-not-include-rp-of-beta-reduce-term
(arg nil)))
:in-theory (e/d () ()))))
(defthm not-include-rp-of-beta-reduce-term-expr
(implies (and (is-lambda term)
(not (include-fnc term 'rp)))
(not (include-fnc (beta-reduce-lambda-expr term) 'rp)))
:hints (("Goal"
:use ((:instance not-include-rp-of-beta-reduce-term-arg=nil
(term (CAR (CDR (CDR (CAR TERM)))))
(keys (CAR (CDR (CAR TERM))))
(vals (CDR TERM))))
:in-theory (e/d (beta-reduce-lambda-expr
is-lambda)
(acl2::beta-reduce-term
not-include-rp-of-beta-reduce-term-arg=nil)))))
)||#
(defthm-valid-sc
(defthmd not-include-rp-means-valid-sc
(implies (and (not (include-fnc term 'rp))
(or (not (include-fnc term 'equals 2))
(not (include-fnc term 'equals))))
(and (valid-sc term a)))
:flag valid-sc)
(defthmd not-include-rp-means-valid-sc-lst
(implies (and (not (include-fnc-subterms subterms 'rp))
(or (not (include-fnc-subterms subterms 'equals 2))
(not (include-fnc-subterms subterms 'equals))))
(and (valid-sc-subterms subterms a)))
:flag valid-sc-subterms)
:hints (("Goal"
:in-theory (e/d (is-rp
valid-sc-nt) ()))))
(defthm-valid-sc-nt
(defthmd not-include-rp-means-valid-sc-nt
(implies (and (not (include-fnc term 'rp))
(or (not (include-fnc term 'equals 2))
(not (include-fnc term 'equals))))
(and (valid-sc-nt term a)))
:flag valid-sc-nt)
(defthmd not-include-rp-means-valid-sc-nt-subterms
(implies (and (not (include-fnc-subterms subterms 'rp))
(or (not (include-fnc-subterms subterms 'equals 2))
(not (include-fnc-subterms subterms 'equals))))
(and (valid-sc-nt-subterms subterms a)))
:flag valid-sc-nt-subterms)
:hints (("Goal"
:in-theory (e/d (is-rp
valid-sc-nt) ()))))
(defthm valid-sc-ex-from-rp
(implies (valid-sc term a)
(valid-sc (ex-from-rp term) a))
:hints (("Goal"
:induct (ex-from-rp term)
:in-theory (e/d (ex-from-rp is-rp) ()))))
(defthm valid-sc-ex-from-rp-2
(implies (EVAL-AND-ALL (CONTEXT-FROM-RP TERM NIL)
A)
(equal (valid-sc (ex-from-rp term) a)
(valid-sc term a)))
:hints (("Goal"
:induct (ex-from-rp term)
:in-theory (e/d (CONTEXT-FROM-RP
ex-from-rp
is-rp) ()))))
(defthm valid-sc-nil
(and (VALID-SC NIL A)
(VALID-SC-BINDINGS NIL A))
:hints (("Goal"
:in-theory (e/d (valid-sc
valid-sc-bindings) ()))))
(encapsulate
nil
(defthm extract-from-rp-pseudo-term-listp
(implies (rp-termp term)
(rp-termp (ex-from-rp TERM)))
:hints (("Goal"
:induct (ex-from-rp TERM)
:in-theory (enable is-rp ex-from-rp))))
(defthm extract-from-synp-pseudo-term-listp
(implies (rp-termp term)
(rp-termp (ex-from-synp TERM)))
:hints (("Goal"
:in-theory (enable is-synp extract-from-synp)))
:rule-classes :forward-chaining)
(local
(defthmd pseudo-termp-lemma2
(implies (rp-termp term)
(not (equal term nil)))))
(local
(defthm stupid-lemma1
(implies (and (rp-termp term)
(should-term-be-in-cons term term2))
(and (ex-from-synp (ex-from-rp (cadr term)))))
:instructions
((:in-theory (e/d (should-term-be-in-cons)
(ex-from-synp)))
(:use (:instance pseudo-termp-lemma2
(term (ex-from-synp (ex-from-rp (cadr term))))))
:promote (:demote 1)
(:dv 1 1)
(:rewrite pseudo-termp-extract-from-synp)
(:change-goal nil t)
(:rewrite extract-from-rp-pseudo-term-listp)
(:change-goal nil t)
(:change-goal nil t)
:expand :s-prop (:demote 2)
(:dive 1)
:s :top
:promote :prove
:top :s)))
(local
(defthm stupid-lemma2
(implies (and (rp-termp term)
(should-term-be-in-cons term term2))
(and (ex-from-synp (ex-from-rp (caddr term)))))
:instructions
((:in-theory (e/d (should-term-be-in-cons)
(ex-from-synp)))
(:use (:instance pseudo-termp-lemma2
(term (ex-from-synp (ex-from-rp (caddr term))))))
:promote (:demote 1)
(:dv 1 1)
(:rewrite pseudo-termp-extract-from-synp)
(:change-goal nil t)
(:rewrite extract-from-rp-pseudo-term-listp)
(:change-goal nil t)
(:change-goal nil t)
:expand :s-prop (:demote 2)
(:dive 1)
:s :top
:promote :prove
:top :s)))
(defthm psuedo-termp2-and-ex-form-synp&rp
(implies (and (rp-termp term)
(should-term-be-in-cons term term2))
(and (ex-from-synp (ex-from-rp (cadr term)))
(ex-from-synp (ex-from-rp (caddr term)))))
:hints (("goal"
:use ((:instance stupid-lemma2)
(:instance stupid-lemma1))
:in-theory (e/d (stupid-lemma2 stupid-lemma1)
(ex-from-synp)))))
(defthm is-if-rp-termp
(implies (and (rp-termp term)
(is-if term))
(and (rp-termp (cadr term))
(rp-termp (caddr term))
(rp-termp (cadddr term))))
:hints (("Goal" :in-theory (enable is-if)))))
(defthm rp-termp-implies-subterms
(implies (and (consp term)
(not (quotep term))
(rp-termp term))
(rp-term-listp (cdr term))))
(defthm valid-sc-subterms-append
(equal (valid-sc-subterms (append x y) a)
(and (valid-sc-subterms x a)
(valid-sc-subterms y a)))
:hints (("Goal"
:in-theory (e/d (valid-sc
append) ()))))
(defthm valid-rulep-implies-valid-sc
(implies (and (valid-rulep rule)
(eval-and-all-nt (rp-hyp rule) a))
(valid-sc-nt (rp-rhs rule) a))
:hints (("Goal"
:use (:instance valid-rulep-sk-necc)
:in-theory (e/d (valid-rulep
not-include-rp-means-valid-sc
not-include-rp-means-valid-sc-nt)
(valid-sc
rp-rhs
rp-hyp
valid-sc-nt
VALID-RULEP-SK
valid-rulep-sk-necc
rule-syntaxp)))))
(defthm-ext-side-conditions
(defthm not-include-rp-EXT-SIDE-CONDITIONS
(implies (NOT (INCLUDE-FNC TERM 'RP))
(equal (EXT-SIDE-CONDITIONS TERM context)
nil))
:flag ext-side-conditions)
(defthm not-include-rp-EXT-SIDE-CONDITIONS-subterms
(implies (NOT (INCLUDE-FNC-SUBTERMS subterms 'RP))
(equal (ext-side-conditions-subterms subterms context)
nil))
:flag ext-side-conditions-subterms)
:hints (("Goal"
:in-theory (e/d (is-rp
ext-side-conditions-subterms
ext-side-conditions)
(EXTRACT-FROM-RP-WITH-CONTEXT)))))
(encapsulate
nil
(defthm not-include-synp
(implies (not (include-fnc term 'synp))
(not (is-synp term)))
:hints (("Goal" :in-theory (enable is-synp))))
(defthm not-include-rp
(implies (not (include-fnc term 'rp))
(not (is-rp term)))
:hints (("Goal" :in-theory (enable is-rp))))
(defthm not-include-ex-from-rp
(implies (not (include-fnc term fnc))
(not (include-fnc (ex-from-rp term) fnc)))
:hints (("Goal"
:in-theory (enable ex-from-rp)
:induct (ex-from-rp term))))
(defthm ex-from-rp-put-term-in-cons
(equal (ex-from-rp (put-term-in-cons term))
(put-term-in-cons term))
:hints (("Goal" :in-theory (enable put-term-in-cons ex-from-rp))))
(defthm quotep-term-with-ex-from-rp
(implies (quotep term)
(quotep (EX-FROM-RP TERM)))
:hints (("Goal" :in-theory (enable ex-from-rp))))
(defthm quotep-term-with-ex-from-synp
(implies (quotep term)
(quotep (EX-FROM-synp TERM)))
:hints (("Goal" :in-theory (enable ex-from-synp))))
(defthm ex-from-synp-put-term-in-cons
(equal (ex-from-synp (put-term-in-cons term))
(put-term-in-cons term))
:hints (("Goal" :in-theory (enable put-term-in-cons ex-from-synp
is-synp))))
(defthm should-term-be-in-cons-lemma2
(implies (should-term-be-in-cons lhs1 term1)
(and (not (should-term-be-in-cons t2 lhs1))
(not (should-term-be-in-cons term1 t3))))
:hints (("Goal" :in-theory (enable should-term-be-in-cons))))
(defthm should-term-be-in-cons-lemma3
(not (should-term-be-in-cons lhs (PUT-TERM-IN-CONS TERM)))
:hints (("Goal" :in-theory (enable put-term-in-cons
should-term-be-in-cons))))
(defthm car-put-term-in-cons
(equal (car (put-term-in-cons term))
'cons)
:hints (("Goal" :in-theory (enable put-term-in-cons))))
(defthmd should-term-be-in-cons-lemma4
(implies (should-term-be-in-cons lhs term)
(equal (car lhs)
'cons))
:hints (("Goal" :in-theory (enable should-term-be-in-cons))))
(defthm is-synp-put-term-cons
(NOT (IS-SYNP (PUT-TERM-IN-CONS term)))
:hints (("Goal" :in-theory (enable put-term-in-cons is-synp))))
(defthm ex-from-rp-cons-cons
(equal (ex-from-rp (cons 'cons x))
(cons 'cons x))
:hints (("Goal" :in-theory (enable ex-from-rp
is-rp))))
(defthm ex-from-rp-put-term-cons
(equal (EX-FROM-RP (PUT-TERM-IN-CONS term))
(put-term-in-cons term))
:hints (("Goal" :in-theory (enable put-term-in-cons
is-rp
ex-from-rp))))
(defthm RP-TERM-LISTP-CDR-PUT-TERM-IN-CONS
(RP-TERM-LISTP (CDR (PUT-TERM-IN-CONS term)))
:hints (("Goal" :in-theory (enable PUT-TERM-IN-CONS)))))
#|(encapsulate
nil
(local
(defthm lemma1
(implies (subtermp-lst x z)
(subtermp-lst x (cons y z)))))
(defthm subtermp-lst-of-the-same
(subtermp-lst x x)))||#
;; (defthm subtermp-ex-from-rp
;; (subtermp (ex-from-rp term) term)
;; :hints (("Goal" :in-theory (enable is-rp ex-from-rp)
;; :induct (ex-from-rp term))))
;; (defthm subtermp-of-the-same
;; (subtermp term term))
(encapsulate
nil
(local
(defthm subsetp-lemma
(implies (subsetp x y)
(subsetp x (cons s y)))))
(defthm context-from-subsetp
(subsetp context (context-from-rp term context) )
:hints (("Goal" :in-theory (enable context-from-rp)
:induct (context-from-rp term context)))))
(encapsulate
nil
(local
(defthm lemma1
(implies
(valid-rulesp lst)
(RULE-LIST-SYNTAXP lst))
:hints (("Goal"
:in-theory (e/d (rule-list-syntaxp)
(valid-rulep-sk
rule-syntaxp))))))
(local
(defthm lemma2
(IMPLIES (AND (VALID-RULES-LIST-LISTP alist))
(RULE-LIST-LIST-SYNTAXP alist))
:hints (("Goal"
:in-theory (e/d () (rule-syntaxp
valid-rulep-sk))))))
(defthm valid-rules-alistp-implies-RULES-ALISTP
(implies (valid-rules-alistp rules-alist)
(rules-alistp rules-alist))
:otf-flg t
:hints (("Goal"
:in-theory (e/d (valid-rules-alistp
RULE-LIST-LIST-SYNTAXP
VALID-RULES-LIST-LISTP
valid-rulesp
rules-alistp
valid-rulep)
(valid-rulep-sk
rule-syntaxp))))))
(defthm VALID-RULESP-implies-RULE-LIST-SYNTAXP
(implies (valid-rulesp rules)
(rule-list-syntaxp rules))
:hints (("Goal"
:in-theory (e/d (valid-rulesp
rule-list-syntaxp)
((:definition falist-consistent)
(:definition rp-termp)
rule-syntaxp
(:definition subsetp-equal))))))
#|(defthm valid-sc-and-is-if
(implies (and (is-if term)
(valid-sc term a))
(and (valid-sc (cadr term) a)
(if (rp-evlt (cadr term) a)
(valid-sc (caddr term) a)
(valid-sc (cadddr term) a))))
:rule-classes :forward-chaining
:hints (("Goal"
:expand (valid-sc term a)
:in-theory (e/d (is-if)
(valid-sc)))))|#
(defthm valid-rules-subsetp
(implies (and (valid-rulesp rules)
(true-listp subrules)
(subsetp subrules rules))
(valid-rulesp subrules))
:hints (("Goal"
:in-theory (disable valid-rulep))))
(defthm-ex-from-rp-all2
(defthm valid-sc-ex-from-rp-all2
(valid-sc (ex-from-rp-all2 term) a)
:flag ex-from-rp-all2)
(defthm valid-sc-subterms-ex-from-rp-all2-lst
(valid-sc-subterms (ex-from-rp-all2-lst lst) a)
:flag ex-from-rp-all2-lst)
:hints (("Goal"
:do-not-induct t
:expand (VALID-SC (CONS (CAR TERM)
(EX-FROM-RP-ALL2-LST (CDR TERM)))
A)
:in-theory (e/d (
EX-FROM-RP-ALL2
is-rp-loose
IS-EQUALS
is-rp
is-if
;;rp-termp-ex-from-rp-all2-lemma
ex-from-rp-all2-lst
)
(ex-from-rp
;;FALIST-CONSISTENT
RP-TERMP-EX-FROM-RP
RP-TERMP-CONS-CAR-TERM-SUBTERMS
)))))
(encapsulate
nil
(local
(defthm rp-evl-of-beta-reduce-lambda-expr-lemma
(implies (AND (ACL2::LAMBDA-EXPR-P acl2::TERM)
(PSEUDO-TERMP acl2::TERM))
(equal (rp-evl (acl2::beta-reduce-lambda-expr acl2::term) acl2::a1)
(rp-evl acl2::term acl2::a1)))
:hints (("Goal"
:use ((:functional-instance
acl2::beta-eval-to-beta-reduce-lambda-expr
(acl2::beta-eval rp-evl)
(acl2::beta-eval-list rp-evl-lst)))
:in-theory (e/d (is-lambda
rp-evl-of-fncall-args)
(acl2::beta-eval-to-beta-reduce-lambda-expr
))))))
(defthm rp-evl-of-beta-reduce-lambda-expr
(implies (AND (rp-termp term)
(is-lambda term))
(equal (rp-evl (acl2::beta-reduce-lambda-expr term) a)
(rp-evl term a)))
:hints (("Goal"
:in-theory (e/d (is-lambda) ()))))
#|(defthm rp-termp-of-beta-reduce-lambda-expr
(implies (and (rp-termp term)
(is-lambda term))
(rp-termp (acl2::beta-reduce-lambda-expr term))))||#
#|(defthm ALL-FALIST-CONSISTENT-of-beta-reduce-lambda-expr
(implies (and (rp-termp term)
(all-falist-consistent term)
(is-lambda term))
(all-falist-consistent (acl2::beta-reduce-lambda-expr term))))||#
#|(defthm rp-syntaxp-of-beta-reduce-lambda-expr
(implies (and (rp-termp term)
(rp-syntaxp term)
(is-lambda term))
(rp-syntaxp (acl2::beta-reduce-lambda-expr term))))||#)
#|(defthm valid-sc-caddr-term
(implies (and (valid-sc term a)
(not (equal (car term) 'if))
(not (equal (car term) 'quote))
(consp term)
(consp (cdr term))
(consp (cddr term)))
(VALID-SC (CADDR TERM) A))
:hints (("Goal"
:expand ((VALID-SC TERM A))
:in-theory (e/d (valid-sc
is-if
is-rp)
()))))||#
#|(defthm valid-sc-cadr-ex-from-rp
(IMPLIES (AND
(CONSP (EX-FROM-RP TERM))
(Not (EQUAL (CAR (EX-FROM-RP TERM)) 'if))
(Not (EQUAL (CAR (EX-FROM-RP TERM)) 'quote))
(CONSP (CDR (EX-FROM-RP TERM)))
(VALID-SC TERM A))
(VALID-SC (CADR (EX-FROM-RP TERM)) A))
:hints (("Goal"
:in-theory (e/d (ex-from-rp
is-if
is-rp) ()))))||#
(defthm valid-sc-ex-from-falist
(implies (valid-sc x a)
(valid-sc (ex-from-falist x) a))
:rule-classes :rewrite
:hints (("Goal"
:expand (ex-from-falist x)
:in-theory (e/d (is-rp
is-if) ()))))
(defthm valid-sc-ex-from-falist-replace
(implies (rp-termp x)
(equal (valid-sc (ex-from-falist x) a)
(valid-sc x a)))
:rule-classes :rewrite
:hints (("Goal"
:expand (ex-from-falist x)
:in-theory (e/d (is-rp
is-if) ()))))
(defthm rp-evl-of-ex-from-falist
(equal (rp-evl (ex-from-falist x) a)
(rp-evl x a))
:hints (("Goal"
:Expand (ex-from-falist x)
:in-theory (e/d () ()))))
(defthm eval-and-all-nt-is-eval-and-all
(implies (not (include-fnc-subterms lst 'list))
(equal (eval-and-all-nt lst a)
(eval-and-all lst a))))
(defthm EVAL-AND-ALL-NT-of-context-from-rp
(implies (and (not (include-fnc-subterms context 'list))
(not (include-fnc term 'list)))
(equal (EVAL-AND-ALL-NT (CONTEXT-FROM-RP TERM context) A)
(EVAL-AND-ALL (CONTEXT-FROM-RP TERM context) A)))
:hints (("Goal"
:induct (CONTEXT-FROM-RP TERM context)
:in-theory (e/d (context-from-rp
eval-and-all-nt-is-eval-and-all
is-rp
rp-evl-of-fncall-args)
()))))
(defthm-valid-sc
(defthm valid-sc-nt-is-valid-sc
(implies (not (include-fnc term 'list))
(equal (valid-sc-nt term a)
(valid-sc term a)))
:flag valid-sc)
(defthm valid-sc-nt-subterms-valid-sc-subterms
(implies (not (include-fnc-subterms subterms 'list))
(equal (valid-sc-nt-subterms subterms a)
(valid-sc-subterms subterms a)))
:flag valid-sc-subterms)
:hints (("Goal"
:expand (VALID-SC-NT TERM A)
:in-theory (e/d (EVAL-AND-ALL-NT-of-context-from-rp) ()))))
(defthm rp-evl-of-trans-list-lemma
(equal (rp-evl (trans-list lst) a)
(rp-evl-lst lst a))
:hints (("Goal"
:do-not-induct t
:induct (trans-list lst)
:in-theory (e/d () ()))))
(local
(defun two-cdr-induct (x y)
(if (or (atom x)
(atom y))
nil
(acons (car x)
(car y)
(two-cdr-induct (cdr x) (cdr y))))))
(local
(defthm rp-evl-of-trans-list-lemma-3
(implies (and (not (consp x))
(not (rp-evl-lst y a)))
(not (rp-evl-lst y a)))))
(defthm rp-evl-of-trans-list-lemma-2
(implies (equal (rp-evl-lst x a1)
(rp-evl-lst y a2))
(equal (equal (rp-evl-lst x a1)
(rp-evl-lst y a2))
t))
:otf-flg t
:hints (("goal"
:do-not-induct t
:induct (two-cdr-induct x y)
:in-theory (e/d () ()))))
(defthm consp-of-RP-EVL-OF-TRANS-LIST
(equal (CONSP (rp-evl-lst lst A))
(consp lst))
:hints (("Goal"
:use ((:instance RP-EVL-LST-OF-ATOM
(ACL2::X-LST lst)
(ACL2::a a)))
:in-theory (e/d ()
(RP-EVL-LST-OF-ATOM)))))
(defthm RP-EVL-OF-TRANS-LIST-nil
(equal (rp-evl-lst nil A)
nil)
:hints (("Goal"
:in-theory (e/d () ()))))
(defthm rp-evlt-of-trans-list-lemma
(equal (rp-evlt (trans-list lst) a)
(rp-evlt-lst lst a))
:hints (("goal" :do-not-induct t
:induct (trans-list lst)
:in-theory (e/d nil nil))))
(defthm valid-sc-of-trans-list-lemma
(implies (valid-sc-subterms lst a)
(valid-sc (trans-list lst) a))
:hints (("goal" :do-not-induct t
:induct (trans-list lst)
:in-theory (e/d (valid-sc is-if is-equals is-rp)
()))))
(defthm rp-state-preservedp-implies-valid-rp-statep
(implies (and ;;(rp-statep rp-state)
(valid-rp-statep rp-state)
(rp-state-preservedp rp-state new-rp-state))
(valid-rp-statep new-rp-state))
:hints (("Goal"
:do-not-induct t
:use ((:instance RP-STATE-PRESERVEDP-SK-necc
(key (valid-rp-statep-witness NEW-RP-STATE))
(OLD-RP-STATE rp-state))
(:instance valid-rp-statep-necc
(key (valid-rp-statep-witness NEW-RP-STATE))))
:expand (valid-rp-statep new-rp-state)
:in-theory (e/d (rp-state-preservedp)
(RP-STATE-PRESERVEDP-SK
VALID-RP-STATEP
VALID-RULESP
RP-STATE-PRESERVEDP-SK
VALID-RP-STATE-SYNTAXP-AUX
valid-rp-statep
(:DEFINITION NOT)
(:TYPE-PRESCRIPTION VALID-RP-STATEP)
(:TYPE-PRESCRIPTION VALID-RULESP)
RP-STATEP)))))
(defthm valid-sc-subterms-of-rev
(equal (valid-sc-subterms (rev x) a)
(valid-sc-subterms x a))
:hints (("Goal"
:in-theory (e/d (rev) ()))))
(defthm eval-and-all-of-rev
(equal (eval-and-all (rev x) a)
(eval-and-all x a))
:hints (("Goal"
:in-theory (e/d (rev) ()))))
|
