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Element-rulename

Element-rulename->get

Get the get field from a element-rulename.

Signature
(element-rulename->get x) → get
Arguments: x — Guard (elementp x).
Returns: get — Type (rulenamep get).

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

Definitions and Theorems

Function: element-rulename->get$inline

(defun element-rulename->get$inline (x)
  (declare (xargs :guard (elementp x)))
  (declare (xargs :guard (equal (element-kind x) :rulename)))
  (let ((__function__ 'element-rulename->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (element-kind x) :rulename)
                      x)))
           (rulename-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: rulenamep-of-element-rulename->get

(defthm rulenamep-of-element-rulename->get
  (b* ((get (element-rulename->get$inline x)))
    (rulenamep get))
  :rule-classes :rewrite)

Theorem: element-rulename->get$inline-of-element-fix-x

(defthm element-rulename->get$inline-of-element-fix-x
  (equal (element-rulename->get$inline (element-fix x))
         (element-rulename->get$inline x)))

Theorem: element-rulename->get$inline-element-equiv-congruence-on-x

(defthm element-rulename->get$inline-element-equiv-congruence-on-x
  (implies (element-equiv x x-equiv)
           (equal (element-rulename->get$inline x)
                  (element-rulename->get$inline x-equiv)))
  :rule-classes :congruence)

Theorem: element-rulename->get-when-wrong-kind

(defthm element-rulename->get-when-wrong-kind
  (implies (not (equal (element-kind x) :rulename))
           (equal (element-rulename->get x)
                  (rulename-fix nil))))