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Undocumented

Svex-alist-eval-equiv!

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

Function: svex-alist-eval-equiv!

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

Definitions and Theorems

Theorem: svex-alist-eval-equiv!-necc

(defthm svex-alist-eval-equiv!-necc
  (implies (not (and (svex-eval-equiv (svex-lookup var x)
                                      (svex-lookup var y))
                     (equal (svex-alist-keys x)
                            (svex-alist-keys y))))
           (not (svex-alist-eval-equiv! x y))))

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

(defthm svex-alist-eval-equiv!-witnessing-witness-rule-correct
  (implies (not ((lambda (var y x)
                   (not (if (svex-eval-equiv (svex-lookup var x)
                                             (svex-lookup var y))
                            (equal (svex-alist-keys x)
                                   (svex-alist-keys y))
                          'nil)))
                 (svex-alist-eval-equiv!-witness x y)
                 y x))
           (svex-alist-eval-equiv! x y))
  :rule-classes nil)

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

(defthm svex-alist-eval-equiv!-instancing-instance-rule-correct
  (implies (not (if (svex-eval-equiv (svex-lookup var x)
                                     (svex-lookup var y))
                    (equal (svex-alist-keys x)
                           (svex-alist-keys y))
                  'nil))
           (not (svex-alist-eval-equiv! x y)))
  :rule-classes nil)

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

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