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Undocumented

Lits-equiv

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

Function: lits-equiv

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

Definitions and Theorems

Theorem: lits-equiv-necc

(defthm lits-equiv-necc
  (implies (not (and (lit-equiv (nth i x) (nth i acl2::y))))
           (not (lits-equiv x acl2::y))))

Theorem: lits-equiv-is-an-equivalence

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