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Declon-declon

Declon-declon->extension

Get the extension field from a declon-declon.

Signature
(declon-declon->extension x) → extension
Arguments: x — Guard (declonp x).
Returns: extension — Type (booleanp extension).

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

Definitions and Theorems

Function: declon-declon->extension$inline

(defun declon-declon->extension$inline (x)
  (declare (xargs :guard (declonp x)))
  (declare (xargs :guard (equal (declon-kind x) :declon)))
  (mbe :logic
       (b* ((x (and (equal (declon-kind x) :declon)
                    x)))
         (bool-fix (car (cdr x))))
       :exec (car (cdr x))))

Theorem: booleanp-of-declon-declon->extension

(defthm booleanp-of-declon-declon->extension
  (b* ((extension (declon-declon->extension$inline x)))
    (booleanp extension))
  :rule-classes :rewrite)

Theorem: declon-declon->extension$inline-of-declon-fix-x

(defthm declon-declon->extension$inline-of-declon-fix-x
  (equal (declon-declon->extension$inline (declon-fix x))
         (declon-declon->extension$inline x)))

Theorem: declon-declon->extension$inline-declon-equiv-congruence-on-x

(defthm declon-declon->extension$inline-declon-equiv-congruence-on-x
  (implies (declon-equiv x x-equiv)
           (equal (declon-declon->extension$inline x)
                  (declon-declon->extension$inline x-equiv)))
  :rule-classes :congruence)

Theorem: declon-declon->extension-when-wrong-kind

(defthm declon-declon->extension-when-wrong-kind
  (implies (not (equal (declon-kind x) :declon))
           (equal (declon-declon->extension x)
                  (bool-fix nil))))