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Implementation-environments

Ienv->char-min

The ACL2 integer value of CHAR_MIN [C17:5.2.4.2.1/1].

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

See char-format->min.

Definitions and Theorems

Function: ienv->char-min

(defun ienv->char-min (ienv)
  (declare (xargs :guard (ienvp ienv)))
  (let ((__function__ 'ienv->char-min))
    (declare (ignorable __function__))
    (char-format->min
         (char+short+int+long+llong-format->char
              (ienv->char+short+int+long+llong-format ienv))
         (char+short+int+long+llong-format->uchar
              (ienv->char+short+int+long+llong-format ienv))
         (char+short+int+long+llong-format->schar
              (ienv->char+short+int+long+llong-format ienv)))))

Theorem: integerp-of-ienv->char-min

(defthm integerp-of-ienv->char-min
  (b* ((min (ienv->char-min ienv)))
    (integerp min))
  :rule-classes :rewrite)

Theorem: ienv->char-min-type-prescription

(defthm ienv->char-min-type-prescription
  (b* ((common-lisp::?min (ienv->char-min ienv)))
    (and (integerp min) (<= min 0)))
  :rule-classes :type-prescription)

Theorem: ienv->char-min-upper-bound

(defthm ienv->char-min-upper-bound
  (b* ((common-lisp::?min (ienv->char-min ienv)))
    (<= min 0))
  :rule-classes ((:linear :trigger-terms ((ienv->char-min ienv)))))

Theorem: ienv->char-min-of-ienv-fix-ienv

(defthm ienv->char-min-of-ienv-fix-ienv
  (equal (ienv->char-min (ienv-fix ienv))
         (ienv->char-min ienv)))

Theorem: ienv->char-min-ienv-equiv-congruence-on-ienv

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