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Values

Value-arithmeticp

Check if a value is arithmetic [C:6.2.5/18].

Signature
(value-arithmeticp val) → yes/no
Arguments: val — Guard (valuep val).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: value-arithmeticp

(defun value-arithmeticp (val)
  (declare (xargs :guard (valuep val)))
  (let ((__function__ 'value-arithmeticp))
    (declare (ignorable __function__))
    (value-realp val)))

Theorem: booleanp-of-value-arithmeticp

(defthm booleanp-of-value-arithmeticp
  (b* ((yes/no (value-arithmeticp val)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: value-arithmeticp-of-value-fix-val

(defthm value-arithmeticp-of-value-fix-val
  (equal (value-arithmeticp (value-fix val))
         (value-arithmeticp val)))

Theorem: value-arithmeticp-value-equiv-congruence-on-val

(defthm value-arithmeticp-value-equiv-congruence-on-val
  (implies (value-equiv val val-equiv)
           (equal (value-arithmeticp val)
                  (value-arithmeticp val-equiv)))
  :rule-classes :congruence)