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Implementation-environments

Sshort-max

Maximum mathematical integer value of type signed short.

Signature
(sshort-max ienv) → val
Arguments: ienv — Guard (ienvp ienv).
Returns: val — Type (natp val).

This depends on the implementation environment.

Definitions and Theorems

Function: sshort-max

(defun sshort-max (ienv)
  (declare (xargs :guard (ienvp ienv)))
  (let ((__function__ 'sshort-max))
    (declare (ignorable __function__))
    (1- (expt 2
              (1- (* 8 (ienv->short-bytes ienv)))))))

Theorem: natp-of-sshort-max

(defthm natp-of-sshort-max
  (b* ((val (sshort-max ienv)))
    (natp val))
  :rule-classes (:rewrite :type-prescription))

Theorem: sshort-max-of-ienv-fix-ienv

(defthm sshort-max-of-ienv-fix-ienv
  (equal (sshort-max (ienv-fix ienv))
         (sshort-max ienv)))

Theorem: sshort-max-ienv-equiv-congruence-on-ienv

(defthm sshort-max-ienv-equiv-congruence-on-ienv
  (implies (ienv-equiv ienv ienv-equiv)
           (equal (sshort-max ienv)
                  (sshort-max ienv-equiv)))
  :rule-classes :congruence)