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Pointed-integers

Ushort-write

Representation of a write of a pointed type unsigned short.

Signature
(ushort-write x) → x
Arguments: x — Guard (ushortp x).
Returns: x — Type (star (ushortp x)).

Definitions and Theorems

Function: ushort-write

(defun ushort-write (x)
  (declare (xargs :guard (ushortp x)))
  (let ((__function__ 'ushort-write))
    (declare (ignorable __function__))
    (ushort-fix x)))

Theorem: return-type-of-ushort-write

(defthm return-type-of-ushort-write
  (b* ((x (ushort-write x)))
    (star (ushortp x)))
  :rule-classes :rewrite)

Theorem: ushortp-of-ushort-write

(defthm ushortp-of-ushort-write
  (b* ((x (ushort-write x))) (ushortp x))
  :rule-classes :rewrite)

Theorem: ushort-write-of-ushort-fix-x

(defthm ushort-write-of-ushort-fix-x
  (equal (ushort-write (ushort-fix x))
         (ushort-write x)))

Theorem: ushort-write-ushort-equiv-congruence-on-x

(defthm ushort-write-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (ushort-write x)
                  (ushort-write x-equiv)))
  :rule-classes :congruence)