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Svstmt-xcond

Svstmt-xcond->cond

Get the cond field from a svstmt-xcond.

Signature
(svstmt-xcond->cond x) → cond
Arguments: x — Guard (svstmt-p x).
Returns: cond — Type (svex-p cond).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: svstmt-xcond->cond$inline

(defun svstmt-xcond->cond$inline (x)
  (declare (xargs :guard (svstmt-p x)))
  (declare (xargs :guard (equal (svstmt-kind x) :xcond)))
  (let ((__function__ 'svstmt-xcond->cond))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (svstmt-kind x) :xcond) x)))
           (svex-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: svex-p-of-svstmt-xcond->cond

(defthm svex-p-of-svstmt-xcond->cond
  (b* ((cond (svstmt-xcond->cond$inline x)))
    (svex-p cond))
  :rule-classes :rewrite)

Theorem: svstmt-xcond->cond$inline-of-svstmt-fix-x

(defthm svstmt-xcond->cond$inline-of-svstmt-fix-x
  (equal (svstmt-xcond->cond$inline (svstmt-fix x))
         (svstmt-xcond->cond$inline x)))

Theorem: svstmt-xcond->cond$inline-svstmt-equiv-congruence-on-x

(defthm svstmt-xcond->cond$inline-svstmt-equiv-congruence-on-x
  (implies (svstmt-equiv x x-equiv)
           (equal (svstmt-xcond->cond$inline x)
                  (svstmt-xcond->cond$inline x-equiv)))
  :rule-classes :congruence)

Theorem: svstmt-xcond->cond-when-wrong-kind

(defthm svstmt-xcond->cond-when-wrong-kind
  (implies (not (equal (svstmt-kind x) :xcond))
           (equal (svstmt-xcond->cond x)
                  (svex-fix nil))))