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4v-operations

4v-or

Four-valued semantics for or gates.

(4v-or a b) returns:

T when either input is T, or
X when either input is X/Z, or
F when both inputs are F.

See 4v-unfloat for an explanation of the Z case.

Definitions and Theorems

Function: 4v-or$inline

(defun 4v-or$inline (a b)
  (declare (xargs :guard t))
  (mbe :logic (4vcases a (t (4vt))
                       (f (4v-unfloat b))
                       (& (4vcases b (t (4vt)) (& (4vx)))))
       :exec (cond ((or (eq a (4vt)) (eq b (4vt))) (4vt))
                   ((and (eq a (4vf)) (eq b (4vf))) (4vf))
                   (t (4vx)))))

Theorem: 4v-equiv-implies-equal-4v-or-2

(defthm 4v-equiv-implies-equal-4v-or-2
  (implies (4v-equiv b b-equiv)
           (equal (4v-or a b) (4v-or a b-equiv)))
  :rule-classes (:congruence))

Theorem: 4v-equiv-implies-equal-4v-or-1

(defthm 4v-equiv-implies-equal-4v-or-1
  (implies (4v-equiv a a-equiv)
           (equal (4v-or a b) (4v-or a-equiv b)))
  :rule-classes (:congruence))