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Repetition

Repetition->element

Get the element field from a repetition.

Signature
(repetition->element x) → element
Arguments: x — Guard (repetitionp x).
Returns: element — Type (elementp element).

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

Definitions and Theorems

Function: repetition->element$inline

(defun repetition->element$inline (x)
  (declare (xargs :guard (repetitionp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'repetition->element))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (element-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: elementp-of-repetition->element

(defthm elementp-of-repetition->element
  (b* ((element (repetition->element$inline x)))
    (elementp element))
  :rule-classes :rewrite)

Theorem: repetition->element$inline-of-repetition-fix-x

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

Theorem: repetition->element$inline-repetition-equiv-congruence-on-x

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