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Representation-of-integer-conversions

Sshort-from-ushort-okp

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

Signature
(sshort-from-ushort-okp x) → yes/no
Arguments: x — Guard (ushortp x).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sshort-from-ushort-okp

(defun sshort-from-ushort-okp (x)
  (declare (xargs :guard (ushortp x)))
  (let ((__function__ 'sshort-from-ushort-okp))
    (declare (ignorable __function__))
    (sshort-integerp (integer-from-ushort x))))

Theorem: booleanp-of-sshort-from-ushort-okp

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

Theorem: sshort-from-ushort-okp-of-ushort-fix-x

(defthm sshort-from-ushort-okp-of-ushort-fix-x
  (equal (sshort-from-ushort-okp (ushort-fix x))
         (sshort-from-ushort-okp x)))

Theorem: sshort-from-ushort-okp-ushort-equiv-congruence-on-x

(defthm sshort-from-ushort-okp-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (sshort-from-ushort-okp x)
                  (sshort-from-ushort-okp x-equiv)))
  :rule-classes :congruence)