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Objdesign-auto

Objdesign-auto->frame

Get the frame field from a objdesign-auto.

Signature
(objdesign-auto->frame x) → frame
Arguments: x — Guard (objdesignp x).
Returns: frame — Type (natp frame).

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

Definitions and Theorems

Function: objdesign-auto->frame$inline

(defun objdesign-auto->frame$inline (x)
  (declare (xargs :guard (objdesignp x)))
  (declare (xargs :guard (equal (objdesign-kind x) :auto)))
  (let ((__function__ 'objdesign-auto->frame))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (objdesign-kind x) :auto)
                      x)))
           (nfix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: natp-of-objdesign-auto->frame

(defthm natp-of-objdesign-auto->frame
  (b* ((frame (objdesign-auto->frame$inline x)))
    (natp frame))
  :rule-classes :rewrite)

Theorem: objdesign-auto->frame$inline-of-objdesign-fix-x

(defthm objdesign-auto->frame$inline-of-objdesign-fix-x
  (equal (objdesign-auto->frame$inline (objdesign-fix x))
         (objdesign-auto->frame$inline x)))

Theorem: objdesign-auto->frame$inline-objdesign-equiv-congruence-on-x

(defthm objdesign-auto->frame$inline-objdesign-equiv-congruence-on-x
  (implies (objdesign-equiv x x-equiv)
           (equal (objdesign-auto->frame$inline x)
                  (objdesign-auto->frame$inline x-equiv)))
  :rule-classes :congruence)

Theorem: objdesign-auto->frame-when-wrong-kind

(defthm objdesign-auto->frame-when-wrong-kind
  (implies (not (equal (objdesign-kind x) :auto))
           (equal (objdesign-auto->frame x)
                  (nfix nil))))