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Amb?-declon/stmt-declon

Amb?-declon/stmt-declon->declon

Get the declon field from a amb?-declon/stmt-declon.

Signature
(amb?-declon/stmt-declon->declon x) → declon
Arguments: x — Guard (amb?-declon/stmt-p x).
Returns: declon — Type (declonp declon).

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

Definitions and Theorems

Function: amb?-declon/stmt-declon->declon$inline

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

Theorem: declonp-of-amb?-declon/stmt-declon->declon

(defthm declonp-of-amb?-declon/stmt-declon->declon
  (b* ((declon (amb?-declon/stmt-declon->declon$inline x)))
    (declonp declon))
  :rule-classes :rewrite)

Theorem: amb?-declon/stmt-declon->declon$inline-of-amb?-declon/stmt-fix-x

(defthm
   amb?-declon/stmt-declon->declon$inline-of-amb?-declon/stmt-fix-x
 (equal
   (amb?-declon/stmt-declon->declon$inline (amb?-declon/stmt-fix x))
   (amb?-declon/stmt-declon->declon$inline x)))

Theorem: amb?-declon/stmt-declon->declon$inline-amb?-declon/stmt-equiv-congruence-on-x

(defthm
 amb?-declon/stmt-declon->declon$inline-amb?-declon/stmt-equiv-congruence-on-x
 (implies (amb?-declon/stmt-equiv x x-equiv)
          (equal (amb?-declon/stmt-declon->declon$inline x)
                 (amb?-declon/stmt-declon->declon$inline x-equiv)))
 :rule-classes :congruence)

Theorem: amb?-declon/stmt-declon->declon-when-wrong-kind

(defthm amb?-declon/stmt-declon->declon-when-wrong-kind
  (implies (not (equal (amb?-declon/stmt-kind x)
                       :declon))
           (equal (amb?-declon/stmt-declon->declon x)
                  (declon-fix nil))))