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Svex-envs-check-ovtests-ok-rec

Signature

(svex-envs-check-ovtests-ok-rec keys x y overridekey-set) → *

Arguments

keys — Guard (svarlist-p keys).

x — Guard (svex-env-p x).

y — Guard (svex-env-p y).

Definitions and Theorems

Function: svex-envs-check-ovtests-ok-rec

(defun svex-envs-check-ovtests-ok-rec (keys x y overridekey-set)
  (declare (xargs :guard (and (svarlist-p keys)
                              (svex-env-p x)
                              (svex-env-p y))))
  (let ((__function__ 'svex-envs-check-ovtests-ok-rec))
    (declare (ignorable __function__))
    (if (atom keys)
        t
      (and (b* ((k (car keys)))
             (or (not (svar-override-p k :test))
                 (if (hons-get (svar-fix k) overridekey-set)
                     (4vec-muxtest-subsetp (svex-env-lookup k x)
                                           (svex-env-lookup k y))
                   (4vec-1mask-equiv (svex-env-lookup k x)
                                     (svex-env-lookup k y)))))
           (svex-envs-check-ovtests-ok-rec (cdr keys)
                                           x y overridekey-set)))))

Theorem: svex-envs-ovtests-ok-of-nils

(defthm svex-envs-ovtests-ok-of-nils
  (svex-envs-ovtests-ok nil nil keys))

Theorem: svex-envs-check-ovtests-ok-rec-correct

(defthm svex-envs-check-ovtests-ok-rec-correct
  (iff (svex-envs-check-ovtests-ok-rec
            keys x y
            (pairlis$ (svarlist-change-override overridekeys :test)
                      nil))
       (svex-envs-ovtests-ok (svex-env-extract keys x)
                             (svex-env-extract keys y)
                             overridekeys)))

Theorem: svex-envs-ovtests-ok-of-extract-superset-1

(defthm svex-envs-ovtests-ok-of-extract-superset-1
  (implies (subsetp-equal (alist-keys (svex-env-fix x))
                          (svarlist-fix keys))
           (iff (svex-envs-ovtests-ok (svex-env-extract keys x)
                                      y overridekeys)
                (svex-envs-ovtests-ok x y overridekeys))))

Theorem: svex-envs-ovtests-ok-of-extract-superset-2

(defthm svex-envs-ovtests-ok-of-extract-superset-2
  (implies (subsetp-equal (alist-keys (svex-env-fix y))
                          (svarlist-fix keys))
           (iff (svex-envs-ovtests-ok x (svex-env-extract keys y)
                                      overridekeys)
                (svex-envs-ovtests-ok x y overridekeys))))

Theorem: svex-envs-check-ovtests-ok-rec-of-svarlist-fix-keys

(defthm svex-envs-check-ovtests-ok-rec-of-svarlist-fix-keys
  (equal (svex-envs-check-ovtests-ok-rec (svarlist-fix keys)
                                         x y overridekey-set)
         (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)))

Theorem: svex-envs-check-ovtests-ok-rec-svarlist-equiv-congruence-on-keys

(defthm
   svex-envs-check-ovtests-ok-rec-svarlist-equiv-congruence-on-keys
 (implies
  (svarlist-equiv keys keys-equiv)
  (equal
   (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)
   (svex-envs-check-ovtests-ok-rec keys-equiv x y overridekey-set)))
 :rule-classes :congruence)

Theorem: svex-envs-check-ovtests-ok-rec-of-svex-env-fix-x

(defthm svex-envs-check-ovtests-ok-rec-of-svex-env-fix-x
  (equal (svex-envs-check-ovtests-ok-rec keys (svex-env-fix x)
                                         y overridekey-set)
         (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)))

Theorem: svex-envs-check-ovtests-ok-rec-svex-env-equiv-congruence-on-x

(defthm
      svex-envs-check-ovtests-ok-rec-svex-env-equiv-congruence-on-x
 (implies
  (svex-env-equiv x x-equiv)
  (equal
   (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)
   (svex-envs-check-ovtests-ok-rec keys x-equiv y overridekey-set)))
 :rule-classes :congruence)

Theorem: svex-envs-check-ovtests-ok-rec-of-svex-env-fix-y

(defthm svex-envs-check-ovtests-ok-rec-of-svex-env-fix-y
  (equal (svex-envs-check-ovtests-ok-rec keys x (svex-env-fix y)
                                         overridekey-set)
         (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)))

Theorem: svex-envs-check-ovtests-ok-rec-svex-env-equiv-congruence-on-y

(defthm
      svex-envs-check-ovtests-ok-rec-svex-env-equiv-congruence-on-y
 (implies
  (svex-env-equiv y y-equiv)
  (equal
   (svex-envs-check-ovtests-ok-rec keys x y overridekey-set)
   (svex-envs-check-ovtests-ok-rec keys x y-equiv overridekey-set)))
 :rule-classes :congruence)