		Search-engine friendly clone of the ACL2 documentation.

Sparseint

Sparseint-unary-minus

Negate a sparseint.

Signature
(sparseint-unary-minus x) → minus
Arguments: x — Guard (sparseint-p x).
Returns: minus — Type (sparseint-p minus).

Definitions and Theorems

Function: sparseint-unary-minus

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

Theorem: sparseint-p-of-sparseint-unary-minus

(defthm sparseint-p-of-sparseint-unary-minus
  (b* ((minus (sparseint-unary-minus x)))
    (sparseint-p minus))
  :rule-classes :rewrite)

Theorem: sparseint-val-of-sparseint-unary-minus

(defthm sparseint-val-of-sparseint-unary-minus
  (b* ((?minus (sparseint-unary-minus x)))
    (equal (sparseint-val minus)
           (- (sparseint-val x)))))

Theorem: sparseint-unary-minus-of-sparseint-fix-x

(defthm sparseint-unary-minus-of-sparseint-fix-x
  (equal (sparseint-unary-minus (sparseint-fix x))
         (sparseint-unary-minus x)))

Theorem: sparseint-unary-minus-sparseint-equiv-congruence-on-x

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