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Undocumented

Nth-lit-equiv

This is a universal equivalence, introduced using ACL2::def-universal-equiv.

Function: nth-lit-equiv

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

Definitions and Theorems

Theorem: nth-lit-equiv-necc

(defthm nth-lit-equiv-necc
  (implies (not (and (equal (nth-lit n x)
                            (nth-lit n acl2::y))))
           (not (nth-lit-equiv x acl2::y))))

Theorem: nth-lit-equiv-is-an-equivalence

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