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Ext-declon-declon

Ext-declon-declon->declon

Get the declon field from a ext-declon-declon.

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

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

Definitions and Theorems

Function: ext-declon-declon->declon$inline

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

Theorem: declonp-of-ext-declon-declon->declon

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

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

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

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

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

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

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