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Maybe-integer-some

Maybe-integer-some->val

Get the fty::val field from a maybe-integer-some.

Signature
(maybe-integer-some->val x) → fty::val
Arguments: x — Guard (maybe-integer-p x).
Returns: fty::val — Type (integerp fty::val).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: maybe-integer-some->val$inline

(defun maybe-integer-some->val$inline (x)
  (declare (xargs :guard (maybe-integer-p x)))
  (declare (xargs :guard x))
  (let ((acl2::__function__ 'maybe-integer-some->val))
    (declare (ignorable acl2::__function__))
    (mbe :logic (b* ((x (and x x))) (ifix x))
         :exec x)))

Theorem: integerp-of-maybe-integer-some->val

(defthm integerp-of-maybe-integer-some->val
  (b* ((fty::val (maybe-integer-some->val$inline x)))
    (integerp fty::val))
  :rule-classes :rewrite)

Theorem: maybe-integer-some->val$inline-of-maybe-integer-fix-x

(defthm maybe-integer-some->val$inline-of-maybe-integer-fix-x
  (equal (maybe-integer-some->val$inline (maybe-integer-fix x))
         (maybe-integer-some->val$inline x)))

Theorem: maybe-integer-some->val$inline-maybe-integer-equiv-congruence-on-x

(defthm
 maybe-integer-some->val$inline-maybe-integer-equiv-congruence-on-x
 (implies (maybe-integer-equiv x x-equiv)
          (equal (maybe-integer-some->val$inline x)
                 (maybe-integer-some->val$inline x-equiv)))
 :rule-classes :congruence)

Theorem: maybe-integer-some->val-when-wrong-kind

(defthm maybe-integer-some->val-when-wrong-kind
  (implies (not x)
           (equal (maybe-integer-some->val x)
                  (ifix nil))))