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Svexlist-rewrite-nrev

Signature

(svexlist-rewrite-nrev x masks 
                       multirefs out-multirefs memo acl2::nrev) 
 
  → 
(mv new-nrev out-multirefs1 memo1)

Arguments

x — Guard (svexlist-p x).

masks — Guard (svex-mask-alist-p masks).

multirefs — Guard (svex-key-alist-p multirefs).

out-multirefs — Guard (svex-key-alist-p out-multirefs).

memo — Guard (svex-svex-memo-p memo).

Returns

out-multirefs1 — Type (svex-key-alist-p out-multirefs1).

memo1 — Type (svex-svex-memo-p memo1).

Definitions and Theorems

Function: svexlist-rewrite-nrev

(defun svexlist-rewrite-nrev
       (x masks
          multirefs out-multirefs memo acl2::nrev)
  (declare (xargs :stobjs (acl2::nrev)))
  (declare (xargs :guard (and (svexlist-p x)
                              (svex-mask-alist-p masks)
                              (svex-key-alist-p multirefs)
                              (svex-key-alist-p out-multirefs)
                              (svex-svex-memo-p memo))))
  (let ((__function__ 'svexlist-rewrite-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (b* ((acl2::nrev (acl2::nrev-fix acl2::nrev)))
          (mv acl2::nrev
              (svex-key-alist-fix out-multirefs)
              (svex-svex-memo-fix memo)))
      (b* (((mv first out-multirefs memo)
            (svex-rewrite (car x)
                          masks multirefs out-multirefs memo))
           (acl2::nrev (acl2::nrev-push first acl2::nrev)))
        (svexlist-rewrite-nrev (cdr x)
                               masks multirefs
                               out-multirefs memo acl2::nrev)))))

Theorem: svex-key-alist-p-of-svexlist-rewrite-nrev.out-multirefs1

(defthm svex-key-alist-p-of-svexlist-rewrite-nrev.out-multirefs1
  (b* (((mv ?new-nrev ?out-multirefs1 ?memo1)
        (svexlist-rewrite-nrev x masks multirefs
                               out-multirefs memo acl2::nrev)))
    (svex-key-alist-p out-multirefs1))
  :rule-classes :rewrite)

Theorem: svex-svex-memo-p-of-svexlist-rewrite-nrev.memo1

(defthm svex-svex-memo-p-of-svexlist-rewrite-nrev.memo1
  (b* (((mv ?new-nrev ?out-multirefs1 ?memo1)
        (svexlist-rewrite-nrev x masks multirefs
                               out-multirefs memo acl2::nrev)))
    (svex-svex-memo-p memo1))
  :rule-classes :rewrite)

Theorem: svexlist-rewrite-nrev-removal

(defthm svexlist-rewrite-nrev-removal
  (b* (((mv ?new-nrev ?out-multirefs1 ?memo1)
        (svexlist-rewrite-nrev x masks multirefs
                               out-multirefs memo acl2::nrev)))
    (b* (((mv out-spec out-multirefs1-spec memo1-spec)
          (svexlist-rewrite x masks multirefs out-multirefs memo)))
      (and (equal new-nrev (append acl2::nrev out-spec))
           (equal out-multirefs1 out-multirefs1-spec)
           (equal memo1 memo1-spec)))))

Theorem: svexlist-rewrite-nrev-of-svexlist-fix-x

(defthm svexlist-rewrite-nrev-of-svexlist-fix-x
 (equal
     (svexlist-rewrite-nrev (svexlist-fix x)
                            masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks multirefs
                            out-multirefs memo acl2::nrev)))

Theorem: svexlist-rewrite-nrev-svexlist-equiv-congruence-on-x

(defthm svexlist-rewrite-nrev-svexlist-equiv-congruence-on-x
 (implies
  (svexlist-equiv x x-equiv)
  (equal
     (svexlist-rewrite-nrev x masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x-equiv masks multirefs
                            out-multirefs memo acl2::nrev)))
 :rule-classes :congruence)

Theorem: svexlist-rewrite-nrev-of-svex-mask-alist-fix-masks

(defthm svexlist-rewrite-nrev-of-svex-mask-alist-fix-masks
 (equal
     (svexlist-rewrite-nrev x (svex-mask-alist-fix masks)
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks multirefs
                            out-multirefs memo acl2::nrev)))

Theorem: svexlist-rewrite-nrev-svex-mask-alist-equiv-congruence-on-masks

(defthm
    svexlist-rewrite-nrev-svex-mask-alist-equiv-congruence-on-masks
 (implies
  (svex-mask-alist-equiv masks masks-equiv)
  (equal
     (svexlist-rewrite-nrev x masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks-equiv multirefs
                            out-multirefs memo acl2::nrev)))
 :rule-classes :congruence)

Theorem: svexlist-rewrite-nrev-of-svex-key-alist-fix-multirefs

(defthm svexlist-rewrite-nrev-of-svex-key-alist-fix-multirefs
  (equal
       (svexlist-rewrite-nrev x masks (svex-key-alist-fix multirefs)
                              out-multirefs memo acl2::nrev)
       (svexlist-rewrite-nrev x masks multirefs
                              out-multirefs memo acl2::nrev)))

Theorem: svexlist-rewrite-nrev-svex-key-alist-equiv-congruence-on-multirefs

(defthm
 svexlist-rewrite-nrev-svex-key-alist-equiv-congruence-on-multirefs
 (implies
  (svex-key-alist-equiv multirefs multirefs-equiv)
  (equal
     (svexlist-rewrite-nrev x masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks multirefs-equiv
                            out-multirefs memo acl2::nrev)))
 :rule-classes :congruence)

Theorem: svexlist-rewrite-nrev-of-svex-key-alist-fix-out-multirefs

(defthm svexlist-rewrite-nrev-of-svex-key-alist-fix-out-multirefs
  (equal (svexlist-rewrite-nrev x masks multirefs
                                (svex-key-alist-fix out-multirefs)
                                memo acl2::nrev)
         (svexlist-rewrite-nrev x masks multirefs
                                out-multirefs memo acl2::nrev)))

Theorem: svexlist-rewrite-nrev-svex-key-alist-equiv-congruence-on-out-multirefs

(defthm
 svexlist-rewrite-nrev-svex-key-alist-equiv-congruence-on-out-multirefs
 (implies
  (svex-key-alist-equiv out-multirefs out-multirefs-equiv)
  (equal
     (svexlist-rewrite-nrev x masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks multirefs
                            out-multirefs-equiv memo acl2::nrev)))
 :rule-classes :congruence)

Theorem: svexlist-rewrite-nrev-of-svex-svex-memo-fix-memo

(defthm svexlist-rewrite-nrev-of-svex-svex-memo-fix-memo
 (equal
      (svexlist-rewrite-nrev x masks multirefs
                             out-multirefs (svex-svex-memo-fix memo)
                             acl2::nrev)
      (svexlist-rewrite-nrev x masks multirefs
                             out-multirefs memo acl2::nrev)))

Theorem: svexlist-rewrite-nrev-svex-svex-memo-equiv-congruence-on-memo

(defthm
      svexlist-rewrite-nrev-svex-svex-memo-equiv-congruence-on-memo
 (implies
  (svex-svex-memo-equiv memo memo-equiv)
  (equal
     (svexlist-rewrite-nrev x masks
                            multirefs out-multirefs memo acl2::nrev)
     (svexlist-rewrite-nrev x masks multirefs
                            out-multirefs memo-equiv acl2::nrev)))
 :rule-classes :congruence)