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Primitive-functions

Eval-imagpart

Evaluation semantics of imagpart.

Signature
(eval-imagpart x) → result
Arguments: x — Guard (valuep x).
Returns: result — Type (valuep result).

Definitions and Theorems

Function: eval-imagpart

(defun eval-imagpart (x)
  (declare (xargs :guard (valuep x)))
  (let ((__function__ 'eval-imagpart))
    (declare (ignorable __function__))
    (value-number (if (value-case x :number)
                      (imagpart (value-number->get x))
                    0))))

Theorem: valuep-of-eval-imagpart

(defthm valuep-of-eval-imagpart
  (b* ((result (eval-imagpart x)))
    (valuep result))
  :rule-classes :rewrite)

Theorem: eval-imagpart-of-value-fix-x

(defthm eval-imagpart-of-value-fix-x
  (equal (eval-imagpart (value-fix x))
         (eval-imagpart x)))

Theorem: eval-imagpart-value-equiv-congruence-on-x

(defthm eval-imagpart-value-equiv-congruence-on-x
  (implies (value-equiv x x-equiv)
           (equal (eval-imagpart x)
                  (eval-imagpart x-equiv)))
  :rule-classes :congruence)