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Sparseint

Sparseint-val

Get the integer value of a sparseint

Signature
(sparseint-val x) → val
Arguments: x — Guard (sparseint-p x).
Returns: val — Type (integerp val).

Definitions and Theorems

Function: sparseint-val

(defun sparseint-val (x)
  (declare (xargs :guard (sparseint-p x)))
  (let ((__function__ 'sparseint-val))
    (declare (ignorable __function__))
    (sparseint$-val (sparseint-fix x))))

Theorem: integerp-of-sparseint-val

(defthm integerp-of-sparseint-val
  (b* ((val (sparseint-val x)))
    (integerp val))
  :rule-classes :type-prescription)

Theorem: sparseint-val-of-sparseint-fix-x

(defthm sparseint-val-of-sparseint-fix-x
  (equal (sparseint-val (sparseint-fix x))
         (sparseint-val x)))

Theorem: sparseint-val-sparseint-equiv-congruence-on-x

(defthm sparseint-val-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-val x)
                  (sparseint-val x-equiv)))
  :rule-classes :congruence)