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Bexp-not

Bexp-not->arg

Get the arg field from a bexp-not.

Signature
(bexp-not->arg x) → arg
Arguments: x — Guard (bexpp x).
Returns: arg — Type (bexpp arg).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: bexp-not->arg$inline

(defun bexp-not->arg$inline (x)
  (declare (xargs :guard (bexpp x)))
  (declare (xargs :guard (equal (bexp-kind x) :not)))
  (let ((__function__ 'bexp-not->arg))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (bexp-kind x) :not) x)))
           (bexp-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: bexpp-of-bexp-not->arg

(defthm bexpp-of-bexp-not->arg
  (b* ((arg (bexp-not->arg$inline x)))
    (bexpp arg))
  :rule-classes :rewrite)

Theorem: bexp-not->arg$inline-of-bexp-fix-x

(defthm bexp-not->arg$inline-of-bexp-fix-x
  (equal (bexp-not->arg$inline (bexp-fix x))
         (bexp-not->arg$inline x)))

Theorem: bexp-not->arg$inline-bexp-equiv-congruence-on-x

(defthm bexp-not->arg$inline-bexp-equiv-congruence-on-x
  (implies (bexp-equiv x x-equiv)
           (equal (bexp-not->arg$inline x)
                  (bexp-not->arg$inline x-equiv)))
  :rule-classes :congruence)

Theorem: bexp-not->arg-when-wrong-kind

(defthm bexp-not->arg-when-wrong-kind
  (implies (not (equal (bexp-kind x) :not))
           (equal (bexp-not->arg x)
                  (bexp-fix nil))))