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Values

Value-realp

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

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

Definitions and Theorems

Function: value-realp

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

Theorem: booleanp-of-value-realp

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

Theorem: value-realp-of-value-fix-val

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

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

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