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Svex-envlists-check-ovtests-ok-rec

Signature

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

Arguments

x — Guard (svex-envlist-p x).

y — Guard (svex-envlist-p y).

Definitions and Theorems

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

(defun svex-envlists-check-ovtests-ok-rec (x y overridekey-set)
  (declare (xargs :guard (and (svex-envlist-p x)
                              (svex-envlist-p y))))
  (let ((__function__ 'svex-envlists-check-ovtests-ok-rec))
    (declare (ignorable __function__))
    (if (atom x)
        (atom y)
      (and (consp y)
           (svex-envs-check-ovtests-ok (car x)
                                       (car y)
                                       overridekey-set)
           (svex-envlists-check-ovtests-ok-rec (cdr x)
                                               (cdr y)
                                               overridekey-set)))))

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

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

Theorem: svex-envlists-check-ovtests-ok-rec-of-svex-envlist-fix-x

(defthm svex-envlists-check-ovtests-ok-rec-of-svex-envlist-fix-x
  (equal (svex-envlists-check-ovtests-ok-rec (svex-envlist-fix x)
                                             y overridekey-set)
         (svex-envlists-check-ovtests-ok-rec x y overridekey-set)))

Theorem: svex-envlists-check-ovtests-ok-rec-svex-envlist-equiv-congruence-on-x

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

Theorem: svex-envlists-check-ovtests-ok-rec-of-svex-envlist-fix-y

(defthm svex-envlists-check-ovtests-ok-rec-of-svex-envlist-fix-y
  (equal (svex-envlists-check-ovtests-ok-rec x (svex-envlist-fix y)
                                             overridekey-set)
         (svex-envlists-check-ovtests-ok-rec x y overridekey-set)))

Theorem: svex-envlists-check-ovtests-ok-rec-svex-envlist-equiv-congruence-on-y

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