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Svex-envlists-ovtestequiv

Signature

(svex-envlists-ovtestequiv x y) → *

Arguments

x — Guard (svex-envlist-p x).

y — Guard (svex-envlist-p y).

Definitions and Theorems

Function: svex-envlists-ovtestequiv

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

Theorem: svex-envlists-ovtestequiv-is-an-equivalence

(defthm svex-envlists-ovtestequiv-is-an-equivalence
  (and (booleanp (svex-envlists-ovtestequiv x y))
       (svex-envlists-ovtestequiv x x)
       (implies (svex-envlists-ovtestequiv x y)
                (svex-envlists-ovtestequiv y x))
       (implies (and (svex-envlists-ovtestequiv x y)
                     (svex-envlists-ovtestequiv y z))
                (svex-envlists-ovtestequiv x z)))
  :rule-classes (:equivalence))

Theorem: svex-envlists-similar-refines-svex-envlists-ovtestequiv

(defthm svex-envlists-similar-refines-svex-envlists-ovtestequiv
  (implies (svex-envlists-similar x y)
           (svex-envlists-ovtestequiv x y))
  :rule-classes (:refinement))

Theorem: svex-envlists-ovtestequiv-refines-svex-envlists-ovtestsimilar

(defthm
      svex-envlists-ovtestequiv-refines-svex-envlists-ovtestsimilar
  (implies (svex-envlists-ovtestequiv x y)
           (svex-envlists-ovtestsimilar x y))
  :rule-classes (:refinement))

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

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

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

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

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

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

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

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