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Svex-envlists-ovtestsubsetp

Signature

(svex-envlists-ovtestsubsetp x y) → *

Arguments

x — Guard (svex-envlist-p x).

y — Guard (svex-envlist-p y).

Definitions and Theorems

Function: svex-envlists-ovtestsubsetp

(defun svex-envlists-ovtestsubsetp (x y)
  (declare (xargs :guard (and (svex-envlist-p x)
                              (svex-envlist-p y))))
  (let ((__function__ 'svex-envlists-ovtestsubsetp))
    (declare (ignorable __function__))
    (if (atom x)
        (atom y)
      (and (consp y)
           (ec-call (svex-envs-ovtestsubsetp (car x)
                                             (car y)))
           (svex-envlists-ovtestsubsetp (cdr x)
                                        (cdr y))))))

Theorem: svex-envlists-ovtestsimilar-implies-iff-svex-envlists-ovtestsubsetp-1

(defthm
 svex-envlists-ovtestsimilar-implies-iff-svex-envlists-ovtestsubsetp-1
 (implies (svex-envlists-ovtestsimilar x x-equiv)
          (iff (svex-envlists-ovtestsubsetp x y)
               (svex-envlists-ovtestsubsetp x-equiv y)))
 :rule-classes (:congruence))

Theorem: svex-envlists-ovtestsimilar-implies-iff-svex-envlists-ovtestsubsetp-2

(defthm
 svex-envlists-ovtestsimilar-implies-iff-svex-envlists-ovtestsubsetp-2
 (implies (svex-envlists-ovtestsimilar y y-equiv)
          (iff (svex-envlists-ovtestsubsetp x y)
               (svex-envlists-ovtestsubsetp x y-equiv)))
 :rule-classes (:congruence))

Theorem: svex-envlists-ovtestsubsetp-of-svex-envlist-fix-x

(defthm svex-envlists-ovtestsubsetp-of-svex-envlist-fix-x
  (equal (svex-envlists-ovtestsubsetp (svex-envlist-fix x)
                                      y)
         (svex-envlists-ovtestsubsetp x y)))

Theorem: svex-envlists-ovtestsubsetp-svex-envlist-equiv-congruence-on-x

(defthm
     svex-envlists-ovtestsubsetp-svex-envlist-equiv-congruence-on-x
  (implies (svex-envlist-equiv x x-equiv)
           (equal (svex-envlists-ovtestsubsetp x y)
                  (svex-envlists-ovtestsubsetp x-equiv y)))
  :rule-classes :congruence)

Theorem: svex-envlists-ovtestsubsetp-of-svex-envlist-fix-y

(defthm svex-envlists-ovtestsubsetp-of-svex-envlist-fix-y
  (equal (svex-envlists-ovtestsubsetp x (svex-envlist-fix y))
         (svex-envlists-ovtestsubsetp x y)))

Theorem: svex-envlists-ovtestsubsetp-svex-envlist-equiv-congruence-on-y

(defthm
     svex-envlists-ovtestsubsetp-svex-envlist-equiv-congruence-on-y
  (implies (svex-envlist-equiv y y-equiv)
           (equal (svex-envlists-ovtestsubsetp x y)
                  (svex-envlists-ovtestsubsetp x y-equiv)))
  :rule-classes :congruence)