		Search-engine friendly clone of the ACL2 documentation.

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))
                 (iff (svex-lookup var x)
                      (svex-lookup var 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))
                     (iff (svex-lookup var x)
                          (svex-lookup var 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))
                            (iff (svex-lookup var x)
                                 (svex-lookup var 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))
                    (iff (svex-lookup var x)
                         (svex-lookup var 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))