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Primitive-functions

Eval-complex-rationalp

Evaluation semantics of complex-rationalp.

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

Definitions and Theorems

Function: eval-complex-rationalp

(defun eval-complex-rationalp (x)
  (declare (xargs :guard (valuep x)))
  (let ((__function__ 'eval-complex-rationalp))
    (declare (ignorable __function__))
    (lift-value (and (value-case x :number)
                     (complex-rationalp (value-number->get x))))))

Theorem: valuep-of-eval-complex-rationalp

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

Theorem: eval-complex-rationalp-of-value-fix-x

(defthm eval-complex-rationalp-of-value-fix-x
  (equal (eval-complex-rationalp (value-fix x))
         (eval-complex-rationalp x)))

Theorem: eval-complex-rationalp-value-equiv-congruence-on-x

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