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Implementation-environments

Slong-min

Minimum mathematical integer value of type signed long.

Signature
(slong-min ienv) → val
Arguments: ienv — Guard (ienvp ienv).
Returns: val — Type (integerp val).

This depends on the implementation environment.

Definitions and Theorems

Function: slong-min

(defun slong-min (ienv)
  (declare (xargs :guard (ienvp ienv)))
  (let ((__function__ 'slong-min))
    (declare (ignorable __function__))
    (- (expt 2 (1- (* 8 (ienv->long-bytes ienv)))))))

Theorem: integerp-of-slong-min

(defthm integerp-of-slong-min
  (b* ((val (slong-min ienv)))
    (integerp val))
  :rule-classes (:rewrite :type-prescription))

Theorem: slong-min-of-ienv-fix-ienv

(defthm slong-min-of-ienv-fix-ienv
  (equal (slong-min (ienv-fix ienv))
         (slong-min ienv)))

Theorem: slong-min-ienv-equiv-congruence-on-ienv

(defthm slong-min-ienv-equiv-congruence-on-ienv
  (implies (ienv-equiv ienv ienv-equiv)
           (equal (slong-min ienv)
                  (slong-min ienv-equiv)))
  :rule-classes :congruence)