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4vmask

4vmask-equiv

Equivalence up to 4vmask-fix.

Definitions and Theorems

Function: 4vmask-equiv$inline

(defun 4vmask-equiv$inline (x y)
  (declare (xargs :guard (and (4vmask-p x) (4vmask-p y))))
  (equal (4vmask-fix x) (4vmask-fix y)))

Theorem: 4vmask-equiv-is-an-equivalence

(defthm 4vmask-equiv-is-an-equivalence
  (and (booleanp (4vmask-equiv x y))
       (4vmask-equiv x x)
       (implies (4vmask-equiv x y)
                (4vmask-equiv y x))
       (implies (and (4vmask-equiv x y)
                     (4vmask-equiv y z))
                (4vmask-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 4vmask-equiv-implies-equal-4vmask-fix-1

(defthm 4vmask-equiv-implies-equal-4vmask-fix-1
  (implies (4vmask-equiv x x-equiv)
           (equal (4vmask-fix x)
                  (4vmask-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 4vmask-fix-under-4vmask-equiv

(defthm 4vmask-fix-under-4vmask-equiv
  (4vmask-equiv (4vmask-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-4vmask-fix-1-forward-to-4vmask-equiv

(defthm equal-of-4vmask-fix-1-forward-to-4vmask-equiv
  (implies (equal (4vmask-fix x) y)
           (4vmask-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-4vmask-fix-2-forward-to-4vmask-equiv

(defthm equal-of-4vmask-fix-2-forward-to-4vmask-equiv
  (implies (equal x (4vmask-fix y))
           (4vmask-equiv x y))
  :rule-classes :forward-chaining)

Theorem: 4vmask-equiv-of-4vmask-fix-1-forward

(defthm 4vmask-equiv-of-4vmask-fix-1-forward
  (implies (4vmask-equiv (4vmask-fix x) y)
           (4vmask-equiv x y))
  :rule-classes :forward-chaining)

Theorem: 4vmask-equiv-of-4vmask-fix-2-forward

(defthm 4vmask-equiv-of-4vmask-fix-2-forward
  (implies (4vmask-equiv x (4vmask-fix y))
           (4vmask-equiv x y))
  :rule-classes :forward-chaining)