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Undocumented

Keys-equiv

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

Function: keys-equiv

(defun keys-equiv (x y)
  (declare (xargs :non-executable t))
  (declare (xargs :guard t))
  (prog2$ (throw-nonexec-error 'keys-equiv
                               (list x y))
          (let ((k (keys-equiv-witness x y)))
            (and (iff (hons-assoc-equal k x)
                      (hons-assoc-equal k y))))))

Definitions and Theorems

Theorem: keys-equiv-necc

(defthm keys-equiv-necc
  (implies (not (and (iff (hons-assoc-equal k x)
                          (hons-assoc-equal k y))))
           (not (keys-equiv x y))))

Theorem: keys-equiv-witnessing-witness-rule-correct

(defthm keys-equiv-witnessing-witness-rule-correct
  (implies (not ((lambda (k y x)
                   (not (iff (hons-assoc-equal k x)
                             (hons-assoc-equal k y))))
                 (keys-equiv-witness x y)
                 y x))
           (keys-equiv x y))
  :rule-classes nil)

Theorem: keys-equiv-instancing-instance-rule-correct

(defthm keys-equiv-instancing-instance-rule-correct
  (implies (not (iff (hons-assoc-equal k x)
                     (hons-assoc-equal k y)))
           (not (keys-equiv x y)))
  :rule-classes nil)

Theorem: keys-equiv-is-an-equivalence

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