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Primitive-functions

Eval-rationalp

Evaluation semantics of rationalp.

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

Definitions and Theorems

Function: eval-rationalp

(defun eval-rationalp (x)
  (declare (xargs :guard (valuep x)))
  (let ((__function__ 'eval-rationalp))
    (declare (ignorable __function__))
    (lift-value (value-case-rational x))))

Theorem: valuep-of-eval-rationalp

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

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

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

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

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