		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-conversions

Slong-from-ulong-okp

Check if a conversion from type unsigned long to type signed long is well-defined.

Signature
(slong-from-ulong-okp x) → yes/no
Arguments: x — Guard (ulongp x).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: slong-from-ulong-okp

(defun slong-from-ulong-okp (x)
  (declare (xargs :guard (ulongp x)))
  (let ((__function__ 'slong-from-ulong-okp))
    (declare (ignorable __function__))
    (slong-integerp (integer-from-ulong x))))

Theorem: booleanp-of-slong-from-ulong-okp

(defthm booleanp-of-slong-from-ulong-okp
  (b* ((yes/no (slong-from-ulong-okp x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: slong-from-ulong-okp-of-ulong-fix-x

(defthm slong-from-ulong-okp-of-ulong-fix-x
  (equal (slong-from-ulong-okp (ulong-fix x))
         (slong-from-ulong-okp x)))

Theorem: slong-from-ulong-okp-ulong-equiv-congruence-on-x

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