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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 "../rp-state-functions")
(include-book "aux-function-lemmas")
(include-book "proof-functions")
(local
(in-theory (enable rp-statep)))
(local
(in-theory (disable equal-of-len-with-constant)))
(defthm integerp-of-RW-STACK-SIZE
(implies (rp-statep rp-state)
(integerp (RW-STACK-SIZE rp-state)))
:hints (("Goal"
:in-theory (e/d (RW-STACK-SIZE
rp-statep)
()))))
(defthm RULES-ALIST-OUTSIDE-IN-GET-of-update-nth
(implies (not (equal index *RULES-ALIST-OUTSIDE-IN-GET*))
(equal (RULES-ALIST-OUTSIDE-IN-GET key
(update-nth index something
rp-state))
(RULES-ALIST-OUTSIDE-IN-GET key
rp-state)))
:hints (("Goal"
:in-theory (e/d (RULES-ALIST-OUTSIDE-IN-GET) ()))))
(defthm RULES-ALIST-inside-out-GET-of-update-nth
(implies (and (not (equal index *RULES-ALIST-inside-out-GET*))
(natp index)
)
(equal (RULES-ALIST-inside-out-GET key
(update-nth index something
rp-state))
(RULES-ALIST-inside-out-GET key
rp-state)))
:hints (("Goal"
:in-theory (e/d (RULES-ALIST-inside-out-GET
zp)
(rp-statep)))))
(defthm valid-rp-statep-of-update-nth
(implies (and
(valid-rp-statep rp-state)
(natp index)
(not (equal index *RULES-ALIST-OUTSIDE-IN-GET*))
(not (equal index *RULES-ALIST-inside-out-GET*)))
(valid-rp-statep (update-nth index val rp-state)))
:hints (("Goal"
:expand ((VALID-RP-STATEP (UPDATE-NTH INDEX VAL RP-STATE)))
:do-not-induct t
:use ((:instance valid-rp-statep-necc
(key (VALID-RP-STATEP-WITNESS (UPDATE-NTH INDEX VAL RP-STATE)))))
:in-theory (e/d (RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-inside-out-GET)
(valid-rp-statep)))))
(Local
(in-theory (disable (:DEFINITION ACL2::APPLY$-BADGEP)
(:REWRITE ACL2::APPLY$-BADGEP-PROPERTIES . 3)
(:REWRITE RP-TERM-LISTP-IS-TRUE-LISTP)
(:REWRITE RP-TERMP-IMPLIES-CDR-LISTP)
(:DEFINITION RP-TERMP))))
(defthm valid-rp-state-syntaxp-of-update-nth
(implies (and
(natp index)
(valid-rp-state-syntaxp rp-state)
(rp-statep (update-nth index val rp-state))
(not (equal index *RULES-ALIST-OUTSIDE-IN-GET*))
(not (equal index *RULES-ALIST-inside-out-GET*)))
(valid-rp-state-syntaxp (update-nth index val rp-state)))
:hints (("Goal"
:expand ((valid-rp-state-syntaxp (UPDATE-NTH INDEX VAL RP-STATE))
(VALID-RP-STATE-SYNTAXP RP-STATE))
:do-not-induct t
:do-not '(preprocess fertilize generalize)
:use ((:instance VALID-RP-STATE-SYNTAXP-aux-necc
(key (VALID-RP-STATE-SYNTAXP-AUX-WITNESS (UPDATE-NTH INDEX VAL RP-STATE)))))
:in-theory (e/d (RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-inside-out-GET)
(valid-rp-statep)))))
(defthm VALID-RP-STATE-SYNTAXP-AUX-of-update-nth
(implies (and
(natp index)
(VALID-RP-STATE-SYNTAXP-AUX rp-state)
(not (equal index *RULES-ALIST-OUTSIDE-IN-GET*))
(not (equal index *RULES-ALIST-inside-out-GET*)))
(VALID-RP-STATE-SYNTAXP-AUX (update-nth index val rp-state)))
:hints (("Goal"
:expand ((valid-rp-state-syntaxp (UPDATE-NTH INDEX VAL RP-STATE))
(VALID-RP-STATE-SYNTAXP RP-STATE))
:do-not-induct t
:use ((:instance VALID-RP-STATE-SYNTAXP-aux-necc
(key (VALID-RP-STATE-SYNTAXP-AUX-WITNESS (UPDATE-NTH INDEX VAL RP-STATE)))))
:in-theory (e/d (RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-inside-out-GET)
(valid-rp-statep)))))
(defthm rp-state-push-to-try-to-rw-stack-is-rp-statep
(implies (rp-statep rp-state)
(rp-statep (mv-nth 1 (rp-state-push-to-try-to-rw-stack rule var-bindings
rp-context
rp-state))))
:hints (("Goal"
:in-theory (e/d (rp-state-push-to-try-to-rw-stack)
()))))
(defthm update-casesplitter-cases-is-rp-statep
(implies (and (rp-statep rp-state)
(rp-term-listp cases))
(rp-statep (update-casesplitter-cases cases rp-state)))
:hints (("goal"
:in-theory (e/d (update-casesplitter-cases)
()))))
(defthm rules-alist-outside-in-get-and-insideout-get-cancel1
(and (equal (rules-alist-outside-in-get key (update-rw-stack-size v rp-state))
(rules-alist-outside-in-get key rp-state))
(equal (rules-alist-outside-in-get key (update-rw-stack v rp-state))
(rules-alist-outside-in-get key rp-state))
(equal (rules-alist-outside-in-get key (update-rule-frame-cnts v rp-state))
(rules-alist-outside-in-get key rp-state))
(equal (rules-alist-outside-in-get key (rules-used-put k v rp-state))
(rules-alist-outside-in-get key rp-state))
#|(equal (rules-alist-outside-in-get key (update-rules-used v rp-state))
(rules-alist-outside-in-get key rp-state))||#
(equal (rules-alist-inside-out-get key (update-rw-stack-size v rp-state))
(rules-alist-inside-out-get key rp-state))
(equal (rules-alist-inside-out-get key (update-rw-stack v rp-state))
(rules-alist-inside-out-get key rp-state))
(equal (rules-alist-inside-out-get key (update-rule-frame-cnts v rp-state))
(rules-alist-inside-out-get key rp-state))
(equal (rules-alist-inside-out-get key (rules-used-put k v rp-state))
(rules-alist-inside-out-get key rp-state))
#|(equal (rules-alist-inside-out-get key (update-rules-used v rp-state))
(rules-alist-inside-out-get key rp-state))||#
)
:hints (("goal"
:in-theory (e/d (rules-alist-outside-in-get
rules-alist-inside-out-get)
()))))
#|(local
(defthm valid-rp-statep-expand
(implies (syntaxp (not (equal rp-state 'rp-state)))
(equal (valid-rp-statep rp-state)
(let
((key (valid-rp-statep-witness rp-state)))
(or
(not (symbolp key))
(and
(valid-rulesp (rules-alist-outside-in-get key rp-state))
(valid-rulesp (rules-alist-inside-out-get key
rp-state)))))))
:hints (("goal"
:in-theory (e/d (valid-rp-statep) ())))))||#
(defthm rp-state-push-to-try-to-rw-stack-is-valid-rp-state-syntaxp
(and (implies (valid-rp-state-syntaxp rp-state)
(valid-rp-state-syntaxp (mv-nth 1 (rp-state-push-to-try-to-rw-stack rule var-bindings
rp-context
rp-state))))
(implies (valid-rp-statep rp-state)
(valid-rp-statep (mv-nth 1 (rp-state-push-to-try-to-rw-stack rule var-bindings
rp-context
rp-state)))))
:hints (("goal"
:in-theory (e/d (rp-state-push-to-try-to-rw-stack
valid-rp-state-syntaxp
update-rw-stack)
(valid-rp-statep
valid-rp-state-syntaxp-aux
)))))
(defthm true-list-of-update-nth
(implies (true-listp lst)
(true-listp (update-nth n x lst))))
(defthm rp-statep-rp-state-push-to-result-to-rw-stack
(implies (rp-statep rp-state)
(rp-statep (rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))
:hints (("goal"
:in-theory (e/d (rp-state-push-to-result-to-rw-stack)
(UNSIGNED-BYTE-P
UPDATE-NTH
(:TYPE-PRESCRIPTION ALISTP)
(:REWRITE DEFAULT-CDR)
(:TYPE-PRESCRIPTION UNSIGNED-BYTE-P)
(:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL)
(:TYPE-PRESCRIPTION TRUE-LISTP-UPDATE-NTH)
(:TYPE-PRESCRIPTION RP-TERM-LISTP)
(:REWRITE NTH-ADD1)
EQUAL-OF-LEN-WITH-CONSTANT
(:DEFINITION HONS-ASSOC-EQUAL))))))
(defret RULES-ALIST-OUTSIDE-IN-GET-of-RP-STATE-PUSH-TO-RESULT-TO-RW-STACK
(and (equal (RULES-ALIST-OUTSIDE-IN-GET key res-rp-state)
(RULES-ALIST-OUTSIDE-IN-GET key rp-state))
(equal (RULES-ALIST-INSIDE-OUT-GET key res-rp-state)
(RULES-ALIST-INSIDE-OUT-GET key rp-state)))
:fn rp-state-push-to-result-to-rw-stack
:hints (("Goal"
:in-theory (e/d (rp-state-push-to-result-to-rw-stack) ()))))
(defthm rp-statep-of-update-rw-stack
(implies (and (rp-statep rp-state)
(alistp v))
(rp-statep (update-rw-stack v rp-state)))
:hints (("goal"
:in-theory (e/d () ()))))
(defthm rp-statep-of-UPDATE-RULE-FRAME-CNTS
(implies (and (rp-statep rp-state)
(alistp v))
(rp-statep (UPDATE-RULE-FRAME-CNTS v rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep) ()))))
(defthm valid-rp-statep-rp-state-push-to-result-to-rw-stack
(implies (valid-rp-statep rp-state)
(valid-rp-statep (rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))
:hints (("goal"
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))))
:in-theory (e/d (;;rp-state-push-to-result-to-rw-stack
valid-rp-statep
;;valid-rp-statep-necc
)
(;;valid-rp-statep
update-rule-frame-cnts
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
rp-statep
rule-frame-cnts
(:rewrite default-cdr)
rw-stack
nfix
hons-acons
hons-get
fix
rw-stack-size
rp-brr
rp-rune$inline
update-rw-stack)))))
(defthm alistp-of-rule-frame-cnts
(implies (rp-statep rp-state)
(alistp (rule-frame-cnts rp-state)))
:hints (("goal"
:in-theory (e/d (rp-statep) ()))))
(defthm alistp-of-rw-stack
(implies (rp-statep rp-state)
(alistp (rw-stack rp-state)))
:hints (("goal"
:in-theory (e/d (rp-statep) ()))))
(defthm valid-rp-state-syntaxp-rp-state-push-to-result-to-rw-stack
(implies (valid-rp-state-syntaxp rp-state)
(valid-rp-state-syntaxp (rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))
:hints (("goal"
:use (
(:instance rp-statep-rp-state-push-to-result-to-rw-stack)
(:instance
valid-rp-state-syntaxp-aux-necc
(key
(valid-rp-state-syntaxp-aux-witness
(rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))))
:in-theory (e/d (;;rp-state-push-to-result-to-rw-stack
valid-rp-state-syntaxp
hons-acons)
(valid-rp-statep
rule-list-syntaxp
update-rule-frame-cnts
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
rp-statep
rule-frame-cnts
(:rewrite default-cdr)
rw-stack
nfix
hons-get
fix
rw-stack-size
rp-brr
rp-rune$inline
update-rw-stack)))))
(defthm rp-statep-rp-stat-add-to-rules-used
(implies (rp-statep rp-state)
(rp-statep (rp-stat-add-to-rules-used rule failed exc-flg rp-state)))
:hints (("goal"
:in-theory (e/d (rp-stat-add-to-rules-used
rp-statep
alistp
hons-acons) ()))))
(defthm valid-rp-statep-rp-stat-add-to-rules-used
(implies (valid-rp-statep rp-state)
(valid-rp-statep (rp-stat-add-to-rules-used rule failed exc-flg rp-state)))
:hints (("goal"
:use ((:instance
valid-rp-statep-necc
(key (valid-rp-statep-witness
(rp-stat-add-to-rules-used rule failed exc-flg rp-state)))))
:in-theory (e/d (rp-stat-add-to-rules-used
rules-alist-outside-in-get
rules-alist-inside-out-get
valid-rp-statep)
(rp-statep
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
;; rules-used-get
(:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(defthm valid-rp-state-syntaxp-rp-stat-add-to-rules-used
(implies (valid-rp-state-syntaxp rp-state)
(valid-rp-state-syntaxp (rp-stat-add-to-rules-used rule failed
exc-flg rp-state)))
:hints (("goal"
:use ((:instance
rp-statep-rp-stat-add-to-rules-used)
(:instance
valid-rp-state-syntaxp-aux-necc
(key (valid-rp-state-syntaxp-aux-witness
(rp-stat-add-to-rules-used rule failed exc-flg rp-state)))))
:in-theory (e/d (rp-stat-add-to-rules-used
valid-rp-state-syntaxp
rules-alist-outside-in-get
rules-alist-inside-out-get
valid-rp-statep)
(rp-statep
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
(:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(defthm rp-statep-rp-state-new-run
(implies (rp-statep rp-state)
(rp-statep (rp-state-new-run rp-state)))
:hints (("goal"
:in-theory (e/d (rp-state-new-run) ()))))
#|(defthm rp-statep-rp-state-new-run
(implies (rp-statep rp-state)
(rp-statep (rp-state-new-run rp-state)))
:hints (("goal"
:in-theory (e/d (rp-state-new-run) ()))))||#
(defthm rp-statep-rp-state-push-meta-to-rw-stack
(implies (rp-statep rp-state)
(rp-statep (rp-state-push-meta-to-rw-stack meta-rule old-term new-term rp-state)))
:hints (("goal"
:in-theory (e/d (rp-statep
rp-state-push-meta-to-rw-stack)
()))))
(defthm rp-statep-of-rules-used-put
(implies (rp-statep rp-state)
(rp-statep (rules-used-put k v rp-state)))
:hints (("goal"
:do-not-induct t
:in-theory (e/d (rules-used-put
rules-alist-outside-in-get
rules-alist-inside-out-get
rp-state-preservedp)
()))))
(defthm rp-state-preservedp-of-rules-used-put
(implies (and (rp-state-preservedp rp-state1 rp-state2))
(rp-state-preservedp rp-state1
(rules-used-put k v rp-state2)))
:hints (("goal"
:do-not-induct t
:expand (rp-state-preservedp-sk rp-state1
(update-nth 5 (cons (cons k v) (nth 5 rp-state2))
rp-state2))
:use ((:instance rp-statep-of-rules-used-put
(rp-state rp-state2))
(:instance rp-state-preservedp-sk-necc
(key (rp-state-preservedp-sk-witness
rp-state1
(update-nth 5 (cons (cons k v) (nth 5 rp-state2))
rp-state2)))
(old-rp-state rp-state1)
(new-rp-state rp-state2)))
:in-theory (e/d (rules-used-put
rules-alist-outside-in-get
rules-alist-inside-out-get
rp-state-preservedp)
(;;rp-statep
rp-statep-of-rules-used-put
rp-state-preservedp-sk)))))
(defthm rp-state-preservedp-rp-stat-add-to-rules-used
(implies (rp-state-preservedp rp-state1 rp-state2)
(rp-state-preservedp rp-state1
(rp-stat-add-to-rules-used rule failed flg
rp-state2)))
:hints (("goal"
:do-not-induct t
:in-theory (e/d (rp-stat-add-to-rules-used
;; rules-alist-outside-in-get
;; rules-alist-inside-out-get
;;rp-state-preservedp
valid-rp-statep)
(rp-statep
rules-used-put
rules-used-get
rules-used-boundp
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
;; rules-used-get
(:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(defthm rp-statep-of-update-rw-stack-size
(implies (and (rp-statep rp-state)
(integerp v)
)
(rp-statep (update-rw-stack-size v rp-state)))
:hints (("goal"
:in-theory (e/d () ()))))
(defthm rp-state-preservedp-of-update-rw-stack-size
(implies (and (rp-state-preservedp rp-state1 rp-state2)
(force (integerp v)))
(rp-state-preservedp rp-state1
(update-rw-stack-size v rp-state2)))
:hints (("goal"
:do-not-induct t
:expand (rp-state-preservedp-sk rp-state1 (update-nth 7 v rp-state2))
:use ((:instance rp-statep-of-update-rw-stack-size
(rp-state rp-state2))
(:instance rp-state-preservedp-sk-necc
(key (rp-state-preservedp-sk-witness rp-state1 (update-nth 7 v rp-state2)))
(old-rp-state rp-state1)
(new-rp-state rp-state2)))
:in-theory (e/d (rules-used-put
update-rw-stack-size
rules-alist-outside-in-get
rules-alist-inside-out-get
rp-state-preservedp)
(;;rp-statep
rp-statep-of-rules-used-put
rp-state-preservedp-sk)))))
(defthm valid-rp-statep-of-update-rw-stack-size
(implies (and (valid-rp-statep rp-state))
(valid-rp-statep (update-rw-stack-size v rp-state)))
:hints (("Goal"
:do-not-induct t
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(update-rw-stack-size v rp-state)))))
:in-theory (e/d (update-rw-stack-size
;;RULES-ALIST-OUTSIDE-IN-GET
;;RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep)
(rp-statep)))))
(defthm VALID-RP-STATE-SYNTAXP-of-update-rw-stack-size
(implies (and (VALID-RP-STATE-SYNTAXP rp-state)
(integerp v))
(VALID-RP-STATE-SYNTAXP (update-rw-stack-size v rp-state)))
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (RP-STATEP
update-rw-stack-size
;;RULES-ALIST-OUTSIDE-IN-GET
;;RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep
VALID-RP-STATE-SYNTAXP)
()))))
(defthm rp-state-preservedp-of-update-rw-stack
(implies (and (rp-state-preservedp rp-state1 rp-state2)
(force (alistp v)))
(rp-state-preservedp rp-state1
(update-rw-stack v rp-state2)))
:hints (("goal"
:do-not-induct t
:expand (rp-state-preservedp-sk rp-state1 (update-nth 8 v rp-state2))
:use ((:instance rp-statep-of-update-rw-stack
(rp-state rp-state2))
(:instance rp-state-preservedp-sk-necc
(key (rp-state-preservedp-sk-witness rp-state1 (update-nth 8 v rp-state2)))
(old-rp-state rp-state1)
(new-rp-state rp-state2)))
:in-theory (e/d (rules-used-put
update-rw-stack-size
rules-alist-outside-in-get
rules-alist-inside-out-get
rp-state-preservedp)
(;;rp-statep
rp-statep-of-rules-used-put
rp-state-preservedp-sk)))))
(defthm valid-rp-statep-of-update-rw-stack
(implies (and (valid-rp-statep rp-state))
(valid-rp-statep (update-rw-stack v rp-state)))
:hints (("Goal"
:do-not-induct t
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(update-rw-stack v rp-state)))))
:in-theory (e/d (update-rw-stack
;;RULES-ALIST-OUTSIDE-IN-GET
;;RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep)
(rp-statep)))))
(defthm VALID-RP-STATE-SYNTAXP-of-update-rw-stack
(implies (and (VALID-RP-STATE-SYNTAXP rp-state)
(ALISTP V))
(VALID-RP-STATE-SYNTAXP (update-rw-stack v rp-state)))
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (VALID-RP-STATE-SYNTAXP
update-rw-stack
RP-STATEP
;;RULES-ALIST-OUTSIDE-IN-GET
;;RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep)
()))))
(defthm rp-state-preservedp-implies-alistp
(implies (rp-state-preservedp rpstate1 rp-state2)
(rp-statep rp-state2))
:hints (("goal"
:in-theory (e/d (rp-state-preservedp) ())))
:rule-classes (:rewrite :forward-chaining))
(defthm rp-state-preservedp-rp-state-push-meta-to-rw-stack
(implies (rp-state-preservedp rp-state1 rp-state2)
(rp-state-preservedp rp-state1
(rp-state-push-meta-to-rw-stack meta-rule old-term new-term
rp-state2)))
:hints (("goal"
:do-not-induct t
:in-theory (e/d (rp-state-push-meta-to-rw-stack
;; rules-alist-outside-in-get
;; rules-alist-inside-out-get
;;rp-state-preservedp
valid-rp-statep
alistp)
(rp-statep
update-rw-stack-size
update-rw-stack
rw-stack-size
rw-stack
rules-used-put
rules-used-get
rules-used-boundp
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
;; rules-used-get
;; (:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(defthm valid-rp-statep-push-meta-to-rw-stack
(implies (valid-rp-statep rp-state)
(valid-rp-statep (rp-state-push-meta-to-rw-stack meta-rule old-term new-term rp-state)))
:hints (("goal"
:do-not-induct t
:in-theory (e/d (rp-state-push-meta-to-rw-stack
;; rules-alist-outside-in-get
;; rules-alist-inside-out-get
;;rp-state-preservedp
alistp)
(valid-rp-statep
rp-statep
update-rw-stack-size
update-rw-stack
rw-stack-size
rw-stack
rules-used-put
rules-used-get
rules-used-boundp
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
;; rules-used-get
;; (:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(local
(defthm dummy-integerp-lemma
(implies (integerp x)
(integerp (1+ x)))))
(defthm valid-rp-state-syntaxp-meta-to-rw-stack
(implies (valid-rp-state-syntaxp rp-state)
(valid-rp-state-syntaxp (rp-state-push-meta-to-rw-stack meta-rule old-term new-term rp-state)))
:hints (("goal"
:do-not-induct t
:in-theory (e/d (rp-state-push-meta-to-rw-stack
;; rules-alist-outside-in-get
;; rules-alist-inside-out-get
;;rp-state-preservedp
alistp)
(VALID-RP-STATE-SYNTAXP
VALID-RP-STATE-SYNTAXP-aux
valid-rp-statep
rp-statep
update-rw-stack-size
update-rw-stack
rw-stack-size
rw-stack
rules-used-put
rules-used-get
rules-used-boundp
;;update-rules-used
(:definition valid-sc-nt)
;; (:rewrite acl2::o-p-o-infp-car)
(:definition eval-and-all-nt)
(:rewrite default-cdr)
;; (:rewrite acl2::o-p-def-o-finp-1)
(:type-prescription o-p)
(:definition rp-hyp$inline)
(:definition count-used-rules-flg)
(:definition hons-acons)
(:definition hons-get)
(:definition nfix)
;; rules-used-get
;; (:definition not)
;;(:definition rules-used)
(:definition show-used-rules-flg)
(:definition rp-rune$inline)
)))))
(defthm valid-rp-state-syntaxp-update-casesplitter-cases-is-rp-statep
(implies (and (valid-rp-state-syntaxp rp-state)
(rp-term-listp cases)
)
(valid-rp-state-syntaxp (update-casesplitter-cases cases rp-state)))
:hints (("goal"
:use ((:instance
valid-rp-state-syntaxp-aux-necc
(key
(valid-rp-state-syntaxp-aux-witness
(update-casesplitter-cases cases rp-state)))))
:in-theory (e/d (update-casesplitter-cases
rules-alist-outside-in-get
rules-alist-inside-out-get
valid-rp-state-syntaxp)
()))))
(defthm rp-state-preservedp-of-update-casesplitter-cases
(implies (and (rp-state-preservedp rp-state1 rp-state2)
(force (rp-term-listp cases)))
(rp-state-preservedp rp-state1
(update-casesplitter-cases cases rp-state2)))
:hints (("Goal"
:do-not-induct t
:expand ((:free (x)
(RP-STATE-PRESERVEDP-SK RP-STATE1 (UPDATE-NTH x CASES RP-STATE2))))
:use ((:instance RP-STATEP-of-UPDATE-RW-STACK
(rp-state rp-state2))
(:instance RP-STATE-PRESERVEDP-SK-necc
(key (RP-STATE-PRESERVEDP-SK-WITNESS RP-STATE1 (update-casesplitter-cases cases rp-state2)))
(old-rp-state rp-state1)
(new-rp-state rp-state2)))
:in-theory (e/d (RULES-USED-PUT
update-casesplitter-cases
RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-INSIDE-OUT-GET
RP-STATE-PRESERVEDP)
(;;rp-statep
RP-STATEP-of-RULES-USED-PUT
rp-state-preservedp-sk)))))
(progn
(defret rp-statep-of-limit-reached-action
(implies (rp-statep rp-state)
(rp-statep res-rp-state))
:fn limit-reached-action
:hints (("Goal"
:in-theory (e/d (limit-reached-action) ()))))
(defret valid-rp-state-syntaxp-of-limit-reached-action
(implies (valid-rp-state-syntaxp rp-state)
(valid-rp-state-syntaxp res-rp-state))
:fn limit-reached-action
:hints (("Goal"
:in-theory (e/d (limit-reached-action) ()))))
(defret valid-rp-statep-of-limit-reached-action
(implies (valid-rp-statep rp-state)
(valid-rp-statep res-rp-state))
:fn limit-reached-action
:hints (("Goal"
:in-theory (e/d (limit-reached-action) ())))))
;;;;;;;;
(defthm RULE-LIST-SYNTAXP-of-RULES-ALIST-OUTSIDE-IN-GET/inside-out-get
(implies (and (valid-rp-state-syntaxp rp-state)
(symbolp key))
(and (rule-list-syntaxp (RULES-ALIST-OUTSIDE-IN-GET key rp-state))
(rule-list-syntaxp (RULES-ALIST-inside-out-GET key rp-state))
))
:hints (("Goal"
:use ((:instance VALID-RP-STATE-SYNTAXP-AUX-necc
))
:in-theory (e/d (valid-rp-state-syntaxp)
()))))
(defret rp-statep-of-post-backchain-ops
(implies (and (rp-statep rp-state))
(rp-statep res-rp-state))
:fn post-backchain-ops
:hints (("Goal"
:in-theory (e/d (post-backchain-ops
rp-statep)
()))))
(defret valid-rp-statep-of-post-backchain-ops
(implies (valid-rp-statep rp-state)
(valid-rp-statep res-rp-state))
:fn post-backchain-ops
:hints (("Goal"
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(POST-BACKCHAIN-OPS BACKCHAIN-ENDS
RP-STATE)))))
:in-theory (e/d (post-backchain-ops
RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep)
(rp-statep)))))
(defret valid-rp-state-syntaxp-of-post-backchain-ops
(implies (and (valid-rp-state-syntaxp rp-state))
(valid-rp-state-syntaxp res-rp-state))
:fn post-backchain-ops
:hints (("Goal"
:use ((:instance rp-statep-of-post-backchain-ops)
(:instance
valid-rp-state-syntaxp-aux-necc
(key
(valid-rp-state-syntaxp-aux-witness
(post-backchain-ops BACKCHAIN-ENDS ;
RP-STATE)))))
:in-theory (e/d (post-backchain-ops
valid-rp-state-syntaxp
rp-statep)
(valid-rp-statep
rp-statep)))))
(defret rp-state-preservedp-of-post-backchain-ops
(implies (rp-state-preservedp rp-state-old rp-state)
(rp-state-preservedp rp-state-old res-rp-state))
:fn post-backchain-ops
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *BACKCHAINING-RULE* NIL RP-STATE)))
:use ((:instance rp-statep-of-post-backchain-ops)
(:instance
RP-STATE-PRESERVEDP-SK-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS RP-STATE-OLD
(UPDATE-NTH *BACKCHAINING-RULE* NIL RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state))
#|(:instance
RP-STATE-PRESERVEDP-SK-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RW-LIMIT-THROWS-ERROR*
OLD-LIMIT-ERROR-SETTING
(UPDATE-NTH *BACKCHAINING-RULE* NIL
(UPDATE-NTH *BACKCHAINING-JUST-STARTED*
NIL RP-STATE)))))
(old-rp-state rp-state-old)
(new-rp-state rp-state))|#)
:in-theory (e/d (post-backchain-ops
RP-STATE-PRESERVEDP
UPDATE-RW-LIMIT-THROWS-ERROR
)
(;;UPDATE-BACKCHAINING-JUST-STARTED
;;UPDATE-BACKCHAINING-RULE
valid-rp-statep
RP-STATE-PRESERVEDP-sk
rp-statep)))))
(defret rp-statep-of-try-to-update-backchaining-rule
(implies (and (rp-statep rp-state))
(rp-statep res-rp-state))
:fn try-to-update-backchaining-rule
:hints (("Goal"
:in-theory (e/d (try-to-update-backchaining-rule
rp-statep)
()))))
(defret valid-rp-statep-of-try-to-update-backchaining-rule
(implies (valid-rp-statep rp-state)
(valid-rp-statep res-rp-state))
:fn try-to-update-backchaining-rule
:hints (("goal"
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(mv-nth 1 (try-to-update-backchaining-rule rule
rp-state))))))
:in-theory (e/d (try-to-update-backchaining-rule
rules-alist-outside-in-get
rules-alist-inside-out-get
valid-rp-statep)
(rp-statep)))))
(defret valid-rp-state-syntaxp-of-try-to-update-backchaining-rule
(implies (and (valid-rp-state-syntaxp rp-state))
(valid-rp-state-syntaxp res-rp-state))
:fn try-to-update-backchaining-rule
:hints (("Goal"
:use ((:instance rp-statep-of-try-to-update-backchaining-rule)
(:instance
valid-rp-state-syntaxp-aux-necc
(key
(valid-rp-state-syntaxp-aux-witness
(try-to-update-backchaining-rule rule
RP-STATE)))))
:in-theory (e/d (try-to-update-backchaining-rule
valid-rp-state-syntaxp
rp-statep)
(valid-rp-statep
rp-statep)))))
(defret rp-statep-of-INCREMENT-RW-STACK-SIZE
(implies (and (rp-statep rp-state))
(rp-statep res-rp-state))
:fn INCREMENT-RW-STACK-SIZE
:hints (("Goal"
:in-theory (e/d (INCREMENT-RW-STACK-SIZE
rp-statep)
()))))
(defret valid-rp-statep-of-INCREMENT-RW-STACK-SIZE
(implies (valid-rp-statep rp-state)
(valid-rp-statep res-rp-state))
:fn INCREMENT-RW-STACK-SIZE
:hints (("Goal"
:use ((:instance
valid-rp-statep-necc
(key
(valid-rp-statep-witness
(INCREMENT-RW-STACK-SIZE RP-STATE)))))
:in-theory (e/d (INCREMENT-RW-STACK-SIZE
RULES-ALIST-OUTSIDE-IN-GET
RULES-ALIST-INSIDE-OUT-GET
valid-rp-statep)
(rp-statep)))))
(defret valid-rp-state-syntaxp-of-INCREMENT-RW-STACK-SIZE
(implies (and (valid-rp-state-syntaxp rp-state)
(booleanp old-limit-error-setting))
(valid-rp-state-syntaxp res-rp-state))
:fn INCREMENT-RW-STACK-SIZE
:hints (("Goal"
:use ((:instance rp-statep-of-INCREMENT-RW-STACK-SIZE)
(:instance
valid-rp-state-syntaxp-aux-necc
(key
(valid-rp-state-syntaxp-aux-witness
(INCREMENT-RW-STACK-SIZE RP-STATE)))))
:in-theory (e/d (INCREMENT-RW-STACK-SIZE
valid-rp-state-syntaxp
rp-statep)
(valid-rp-statep
rp-statep)))))
(defret RP-STATE-PRESERVEDP-of-INCREMENT-RW-STACK-SIZE
(implies (rp-state-preservedp rp-state-old rp-state)
(rp-state-preservedp rp-state-old res-rp-state))
:fn INCREMENT-RW-STACK-SIZE
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *RW-STACK-SIZE*
(+ 1 (NTH *RW-STACK-SIZE* RP-STATE))
RP-STATE)))
:use ((:instance rp-statep-of-INCREMENT-RW-STACK-SIZE)
(:instance
rp-state-preservedp-sk-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RW-STACK-SIZE*
(+ 1 (NTH *RW-STACK-SIZE* RP-STATE))
RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state)))
:in-theory (e/d (INCREMENT-RW-STACK-SIZE
RP-STATE-PRESERVEDP
)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
(progn
(defthm rp-statep-of-update-rw-context-disabled
(implies (and (rp-statep rp-state)
(booleanp flg))
(rp-statep (UPDATE-RW-CONTEXT-DISABLED flg rp-state)))
:hints (("Goal"
:in-theory (e/d () ()))))
(defthm valid-rp-state-syntaxp-update-rw-context-disabled
(implies (and (valid-rp-state-syntaxp rp-state)
(booleanp flg))
(valid-rp-state-syntaxp (UPDATE-RW-CONTEXT-DISABLED flg
rp-state)))
:hints (("Goal"
:in-theory (e/d (VALID-RP-STATE-SYNTAXP) ()))))
(defthm valid-rp-statep-update-rw-context-disabled
(implies (and (valid-rp-statep rp-state)
(booleanp flg))
(valid-rp-statep (UPDATE-RW-CONTEXT-DISABLED flg rp-state)))
:hints (("Goal"
:in-theory (e/d () ()))))
(defthm RP-STATE-PRESERVEDP-of-UPDATE-RW-CONTEXT-DISABLED
(implies (and (rp-state-preservedp rp-state-old rp-state)
(booleanp flg))
(rp-state-preservedp rp-state-old (UPDATE-RW-CONTEXT-DISABLED flg rp-state)))
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *RW-CONTEXT-DISABLED* FLG RP-STATE)))
:use ((:instance rp-statep-of-update-rw-context-disabled)
(:instance
rp-state-preservedp-sk-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RW-CONTEXT-DISABLED* FLG RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state)))
:in-theory (e/d (
RP-STATE-PRESERVEDP
UPDATE-RW-CONTEXT-DISABLED)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
(in-theory (disable update-rw-context-disabled)))
(progn
(defthm UPDATE-RW-LIMIT-THROWS-ERROR-rp-statep
(implies (and (rp-statep rp-state)
(booleanp flg))
(rp-statep (update-rw-limit-throws-error flg rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep
UPDATE-RW-LIMIT-THROWS-ERROR) ()))))
(defthm RP-STATE-PRESERVEDP-of-update-rw-limit-throws-error
(implies (and (rp-state-preservedp rp-state-old rp-state)
(booleanp flg))
(rp-state-preservedp rp-state-old (update-rw-limit-throws-error flg rp-state)))
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *RW-LIMIT-THROWS-ERROR* FLG RP-STATE)))
:use ((:instance UPDATE-RW-LIMIT-THROWS-ERROR-rp-statep)
(:instance
rp-state-preservedp-sk-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RW-LIMIT-THROWS-ERROR* FLG RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state)))
:in-theory (e/d (
RP-STATE-PRESERVEDP
update-rw-limit-throws-error)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
)
(progn
(defthm UPDATE-RW-LIMIT-THROWS-ERROR-rp-statep
(implies (and (rp-statep rp-state)
(booleanp flg))
(rp-statep (update-rw-limit-throws-error flg rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep
UPDATE-RW-LIMIT-THROWS-ERROR) ()))))
(defthm RP-STATE-PRESERVEDP-of-update-rw-limit-throws-error
(implies (and (rp-state-preservedp rp-state-old rp-state)
(booleanp flg))
(rp-state-preservedp rp-state-old (update-rw-limit-throws-error flg rp-state)))
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *RW-LIMIT-THROWS-ERROR* FLG RP-STATE)))
:use ((:instance UPDATE-RW-LIMIT-THROWS-ERROR-rp-statep)
(:instance
rp-state-preservedp-sk-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RW-LIMIT-THROWS-ERROR* FLG RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state)))
:in-theory (e/d (
RP-STATE-PRESERVEDP
update-rw-limit-throws-error)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
)
(progn
(defthm valid-rp-state-syntaxp-UPDATE-RULE-FRAME-CNTS
(implies (and (valid-rp-state-syntaxp rp-state)
(alistp v))
(valid-rp-state-syntaxp (UPDATE-RULE-FRAME-CNTS v
rp-state)))
:hints (("Goal"
:use ((:instance rp-statep-of-UPDATE-RULE-FRAME-CNTS))
:in-theory (e/d (VALID-RP-STATE-SYNTAXP) ()))))
(defthm valid-rp-statep-UPDATE-RULE-FRAME-CNTS
(implies (and (valid-rp-statep rp-state)
(alistp v))
(valid-rp-statep (UPDATE-RULE-FRAME-CNTS v rp-state)))
:hints (("Goal"
:in-theory (e/d () ()))))
(defthm RP-STATE-PRESERVEDP-of-UPDATE-RULE-FRAME-CNTS
(implies (and (rp-state-preservedp rp-state-old rp-state)
(alistp v))
(rp-state-preservedp rp-state-old (UPDATE-RULE-FRAME-CNTS v rp-state)))
:hints (("Goal"
:do-not-induct t
:expand ((RP-STATE-PRESERVEDP-SK RP-STATE-OLD
(UPDATE-NTH *RULE-FRAME-CNTS* v RP-STATE)))
:use ((:instance rp-statep-of-UPDATE-RULE-FRAME-CNTS)
(:instance
rp-state-preservedp-sk-necc
(key
(RP-STATE-PRESERVEDP-SK-WITNESS
RP-STATE-OLD
(UPDATE-NTH *RULE-FRAME-CNTS* v RP-STATE)))
(old-rp-state rp-state-old)
(new-rp-state rp-state)))
:in-theory (e/d (
RP-STATE-PRESERVEDP
UPDATE-RULE-FRAME-CNTS)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
(in-theory (disable UPDATE-RULE-FRAME-CNTS)))
(defthm RP-STATE-PRESERVEDP-of-rp-state-push-to-result-to-rw-stack
(implies (and (rp-state-preservedp rp-state-old rp-state))
(rp-state-preservedp rp-state-old (rp-state-push-to-result-to-rw-stack rule
index
failed
old-term
new-term
rp-state)))
:hints (("Goal"
:expand ((RP-STATE-PRESERVEDP RP-STATE-OLD RP-STATE))
:use ((:instance rp-statep-rp-state-push-to-result-to-rw-stack)
#|(:instance
rp-state-preservedp-sk-necc ;
(key ;
(RP-STATE-PRESERVEDP-SK-WITNESS ;
RP-STATE-OLD ;
(UPDATE-NTH *RW-STACK* ;
(CONS (LIST INDEX (LIST :TYPE FAILED) ;
(LIST :RUNE (CDDDR RULE)) ;
(LIST :NEW-TERM NEW-TERM) ;
(LIST :OLD-TERM OLD-TERM)) ;
(NTH *RW-STACK* RP-STATE)) ;
(UPDATE-NTH *RULE-FRAME-CNTS* ;
(CONS (CONS (CDDDR RULE) ;
(+ -1 (- INDEX) ;
(NTH *RW-STACK-SIZE* RP-STATE))) ;
(NTH *RULE-FRAME-CNTS* RP-STATE)) ;
RP-STATE)))) ;
(old-rp-state rp-state-old) ;
(new-rp-state rp-state))|#)
:in-theory (e/d (alistp
;;RP-STATE-PRESERVEDP
rp-state-push-to-result-to-rw-stack)
(RW-STACK-SIZE
RW-STACK
RULE-FRAME-CNTS
valid-rp-statep
UPDATE-RULE-FRAME-CNTS
UPDATE-RW-STACK
RP-STATE-PRESERVEDP-SK
rp-statep)))))
(defret RP-STATE-PRESERVEDP-of-limit-reached-action
(implies (rp-state-preservedp rp-state-old rp-state)
(rp-state-preservedp rp-state-old res-rp-state))
:fn limit-reached-action
:hints (("Goal"
:in-theory (e/d (limit-reached-action
INCREMENT-RW-STACK-SIZE
;;RP-STATE-PRESERVEDP
)
(valid-rp-statep
RP-STATE-PRESERVEDP-SK
rp-statep)))))
(defthm rp-statep-of-update-orig-conjecture
(implies (and (rp-statep rp-state)
(rp-termp x))
(rp-statep (update-orig-conjecture x rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep) ()))))
(encapsulate
nil
(local
(include-book "arithmetic-3/top" :dir :system))
(local
(in-theory (disable UPDATE-NTH)))
(defthm RW-RECENT-TERMSP-of-update-nth
(implies (RW-RECENT-TERMSP lst)
(RW-RECENT-TERMSP (UPDATE-NTH key val lst)))
:hints (("Goal"
:in-theory (e/d (UPDATE-NTH) ()))))
(defthm rp-statep-of-PUSH-TO-RW-RECENT-TERMS
(implies (and (rp-statep rp-state))
(rp-statep (PUSH-TO-RW-RECENT-TERMS x rp-state)))
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (rp-statep
RW-RECENT-TERMSP
PUSH-TO-RW-RECENT-TERMS)
(mod floor)))))
(defthm valid-rp-state-syntaxp-PUSH-TO-RW-RECENT-TERMS
(implies (and (valid-rp-state-syntaxp rp-state))
(valid-rp-state-syntaxp (PUSH-TO-RW-RECENT-TERMS x rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep
PUSH-TO-RW-RECENT-TERMS
VALID-RP-STATE-SYNTAXP)
()))))
(defthm valid-rp-statep-PUSH-TO-RW-RECENT-TERMS
(implies (and (valid-rp-statep rp-state))
(valid-rp-statep (PUSH-TO-RW-RECENT-TERMS x rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-statep
PUSH-TO-RW-RECENT-TERMS
valid-rp-statep)
()))))
)
|
