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Representation-of-integer-operations

Minus-slong-okp

Check if the unary minus of a value of type signed long is well-defined.

Definitions and Theorems

Function: minus-slong-okp

(defun minus-slong-okp (x)
  (declare (xargs :guard (and (slongp x))))
  (slong-integerp (- (integer-from-slong x))))

Theorem: booleanp-of-minus-slong-okp

(defthm booleanp-of-minus-slong-okp
  (booleanp (minus-slong-okp x)))

Theorem: minus-slong-okp-of-slong-fix-x

(defthm minus-slong-okp-of-slong-fix-x
  (equal (minus-slong-okp (slong-fix x))
         (minus-slong-okp x)))

Theorem: minus-slong-okp-slong-equiv-congruence-on-x

(defthm minus-slong-okp-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (minus-slong-okp x)
                  (minus-slong-okp x-equiv)))
  :rule-classes :congruence)