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Undocumented

Nth-equiv

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

Function: nth-equiv

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

Definitions and Theorems

Theorem: nth-equiv-necc

(defthm nth-equiv-necc
  (implies (not (and (equal (nth n x) (nth n y))))
           (not (nth-equiv x y))))

Theorem: nth-equiv-is-an-equivalence

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