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Undocumented

Svex-eval-equiv

This is a universal equivalence, introduced using def-universal-equiv.

Function: svex-eval-equiv

(defun svex-eval-equiv (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (declare (xargs :non-executable t))
  (prog2$ (acl2::throw-nonexec-error 'svex-eval-equiv
                                     (list x y))
          (let ((env (svex-eval-equiv-witness x y)))
            (and (equal (svex-eval x env)
                        (svex-eval y env))))))

Definitions and Theorems

Theorem: svex-eval-equiv-necc

(defthm svex-eval-equiv-necc
  (implies (not (and (equal (svex-eval x env)
                            (svex-eval y env))))
           (not (svex-eval-equiv x y))))

Theorem: svex-eval-equiv-witnessing-witness-rule-correct

(defthm svex-eval-equiv-witnessing-witness-rule-correct
  (implies (not ((lambda (env y x)
                   (not (equal (svex-eval x env)
                               (svex-eval y env))))
                 (svex-eval-equiv-witness x y)
                 y x))
           (svex-eval-equiv x y))
  :rule-classes nil)

Theorem: svex-eval-equiv-instancing-instance-rule-correct

(defthm svex-eval-equiv-instancing-instance-rule-correct
  (implies (not (equal (svex-eval x env)
                       (svex-eval y env)))
           (not (svex-eval-equiv x y)))
  :rule-classes nil)

Theorem: svex-eval-equiv-is-an-equivalence

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