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Declor/absdeclor-absdeclor

Declor/absdeclor-absdeclor->absdeclor

Get the absdeclor field from a declor/absdeclor-absdeclor.

Signature
(declor/absdeclor-absdeclor->absdeclor x) → absdeclor
Arguments: x — Guard (declor/absdeclor-p x).
Returns: absdeclor — Type (absdeclorp absdeclor).

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

Definitions and Theorems

Function: declor/absdeclor-absdeclor->absdeclor$inline

(defun declor/absdeclor-absdeclor->absdeclor$inline (x)
  (declare (xargs :guard (declor/absdeclor-p x)))
  (declare (xargs :guard (equal (declor/absdeclor-kind x)
                                :absdeclor)))
  (mbe :logic
       (b* ((x (and (equal (declor/absdeclor-kind x)
                           :absdeclor)
                    x)))
         (absdeclor-fix (cdr x)))
       :exec (cdr x)))

Theorem: absdeclorp-of-declor/absdeclor-absdeclor->absdeclor

(defthm absdeclorp-of-declor/absdeclor-absdeclor->absdeclor
  (b* ((absdeclor (declor/absdeclor-absdeclor->absdeclor$inline x)))
    (absdeclorp absdeclor))
  :rule-classes :rewrite)

Theorem: declor/absdeclor-absdeclor->absdeclor$inline-of-declor/absdeclor-fix-x

(defthm
 declor/absdeclor-absdeclor->absdeclor$inline-of-declor/absdeclor-fix-x
 (equal (declor/absdeclor-absdeclor->absdeclor$inline
             (declor/absdeclor-fix x))
        (declor/absdeclor-absdeclor->absdeclor$inline x)))

Theorem: declor/absdeclor-absdeclor->absdeclor$inline-declor/absdeclor-equiv-congruence-on-x

(defthm
 declor/absdeclor-absdeclor->absdeclor$inline-declor/absdeclor-equiv-congruence-on-x
 (implies
     (declor/absdeclor-equiv x x-equiv)
     (equal (declor/absdeclor-absdeclor->absdeclor$inline x)
            (declor/absdeclor-absdeclor->absdeclor$inline x-equiv)))
 :rule-classes :congruence)

Theorem: declor/absdeclor-absdeclor->absdeclor-when-wrong-kind

(defthm declor/absdeclor-absdeclor->absdeclor-when-wrong-kind
  (implies (not (equal (declor/absdeclor-kind x)
                       :absdeclor))
           (equal (declor/absdeclor-absdeclor->absdeclor x)
                  (absdeclor-fix nil))))