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4vec

4vec->lower

Raw accessor for the lower integer from a 4vec.

Signature
(4vec->lower x) → lower
Arguments: x — Guard (4vec-p x).
Returns: lower — Type (integerp lower).

Definitions and Theorems

Function: 4vec->lower$inline

(defun 4vec->lower$inline (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec->lower))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (ifix (cdr x))
           (if (integerp x) x 0))
         :exec (if (consp x) (cdr x) x))))

Theorem: integerp-of-4vec->lower

(defthm integerp-of-4vec->lower
  (b* ((lower (4vec->lower$inline x)))
    (integerp lower))
  :rule-classes (:rewrite :type-prescription))

Theorem: 4vec->lower-of-4vec

(defthm 4vec->lower-of-4vec
  (equal (4vec->lower (4vec upper lower))
         (ifix lower)))

Theorem: 4vec->lower-of-4vec-fix

(defthm 4vec->lower-of-4vec-fix
  (equal (4vec->lower (4vec-fix x))
         (4vec->lower x)))

Theorem: 4vec-equiv-implies-equal-4vec->lower-1

(defthm 4vec-equiv-implies-equal-4vec->lower-1
  (implies (4vec-equiv x x-equiv)
           (equal (4vec->lower x)
                  (4vec->lower x-equiv)))
  :rule-classes (:congruence))