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Pointed-integers

Sshort-write

Representation of a write of a pointed type signed short.

Signature
(sshort-write x) → x
Arguments: x — Guard (sshortp x).
Returns: x — Type (star (sshortp x)).

Definitions and Theorems

Function: sshort-write

(defun sshort-write (x)
  (declare (xargs :guard (sshortp x)))
  (let ((__function__ 'sshort-write))
    (declare (ignorable __function__))
    (sshort-fix x)))

Theorem: return-type-of-sshort-write

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

Theorem: sshortp-of-sshort-write

(defthm sshortp-of-sshort-write
  (b* ((x (sshort-write x))) (sshortp x))
  :rule-classes :rewrite)

Theorem: sshort-write-of-sshort-fix-x

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

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

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