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• 4vmask

4vmask-subsumes

(4vmask-subsumes x y) checks whether the 4vmask x cares about strictly more bits than y cares about.

Signature

(4vmask-subsumes x y) → subsumesp

Arguments

x — Guard (4vmask-p x).

y — Guard (4vmask-p y).

Returns

subsumesp — Type (booleanp subsumesp).

Definitions and Theorems

Function: 4vmask-subsumes$inline

(defun 4vmask-subsumes$inline (x y)
  (declare (xargs :guard (and (4vmask-p x) (4vmask-p y))))
  (let ((__function__ '4vmask-subsumes))
    (declare (ignorable __function__))
    (not (sparseint-test-bitandc1 (4vmask-fix x)
                                  (4vmask-fix y)))))

Theorem: booleanp-of-4vmask-subsumes

(defthm booleanp-of-4vmask-subsumes
  (b* ((subsumesp (4vmask-subsumes$inline x y)))
    (booleanp subsumesp))
  :rule-classes :type-prescription)

Theorem: 4vmask-subsumes$inline-of-4vmask-fix-x

(defthm 4vmask-subsumes$inline-of-4vmask-fix-x
  (equal (4vmask-subsumes$inline (4vmask-fix x)
                                 y)
         (4vmask-subsumes$inline x y)))

Theorem: 4vmask-subsumes$inline-4vmask-equiv-congruence-on-x

(defthm 4vmask-subsumes$inline-4vmask-equiv-congruence-on-x
  (implies (4vmask-equiv x x-equiv)
           (equal (4vmask-subsumes$inline x y)
                  (4vmask-subsumes$inline x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vmask-subsumes$inline-of-4vmask-fix-y

(defthm 4vmask-subsumes$inline-of-4vmask-fix-y
  (equal (4vmask-subsumes$inline x (4vmask-fix y))
         (4vmask-subsumes$inline x y)))

Theorem: 4vmask-subsumes$inline-4vmask-equiv-congruence-on-y

(defthm 4vmask-subsumes$inline-4vmask-equiv-congruence-on-y
  (implies (4vmask-equiv y y-equiv)
           (equal (4vmask-subsumes$inline x y)
                  (4vmask-subsumes$inline x y-equiv)))
  :rule-classes :congruence)

Theorem: 4vmask-subsumes-implies-masks-equal

(defthm 4vmask-subsumes-implies-masks-equal
  (implies (and (4vmask-subsumes m1 m2)
                (equal (4vec-mask m1 x)
                       (4vec-mask m1 y)))
           (equal (equal (4vec-mask m2 x)
                         (4vec-mask m2 y))
                  t)))

Theorem: 4vmask-subsumes-neg-1-implies-fixes

(defthm 4vmask-subsumes-neg-1-implies-fixes
  (implies (and (4vmask-subsumes m1 -1)
                (equal (4vec-mask m1 x)
                       (4vec-mask m1 y)))
           (equal (equal (4vec-fix x) (4vec-fix y))
                  t)))

Theorem: 4vmask-subsumes-trans-1

(defthm 4vmask-subsumes-trans-1
  (implies (and (4vmask-subsumes a b)
                (4vmask-subsumes b c))
           (4vmask-subsumes a c)))

Theorem: 4vmask-subsumes-trans-2

(defthm 4vmask-subsumes-trans-2
  (implies (and (4vmask-subsumes b c)
                (4vmask-subsumes a b))
           (4vmask-subsumes a c)))

Theorem: 4vmask-subsumes-self

(defthm 4vmask-subsumes-self
  (4vmask-subsumes x x))