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Natoption/natoptionlist-list

Natoption/natoptionlist-list->get

Get the get field from a natoption/natoptionlist-list.

Signature
(natoption/natoptionlist-list->get x) → get
Arguments: x — Guard (natoption/natoptionlist-p x).
Returns: get — Type (nat-option-listp get).

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

Definitions and Theorems

Function: natoption/natoptionlist-list->get$inline

(defun natoption/natoptionlist-list->get$inline (x)
  (declare (xargs :guard (natoption/natoptionlist-p x)))
  (declare (xargs :guard (equal (natoption/natoptionlist-kind x)
                                :list)))
  (let ((__function__ 'natoption/natoptionlist-list->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (natoption/natoptionlist-kind x)
                             :list)
                      x)))
           (nat-option-list-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: nat-option-listp-of-natoption/natoptionlist-list->get

(defthm nat-option-listp-of-natoption/natoptionlist-list->get
  (b* ((get (natoption/natoptionlist-list->get$inline x)))
    (nat-option-listp get))
  :rule-classes :rewrite)

Theorem: natoption/natoptionlist-list->get$inline-of-natoption/natoptionlist-fix-x

(defthm
 natoption/natoptionlist-list->get$inline-of-natoption/natoptionlist-fix-x
 (equal (natoption/natoptionlist-list->get$inline
             (natoption/natoptionlist-fix x))
        (natoption/natoptionlist-list->get$inline x)))

Theorem: natoption/natoptionlist-list->get$inline-natoption/natoptionlist-equiv-congruence-on-x

(defthm
 natoption/natoptionlist-list->get$inline-natoption/natoptionlist-equiv-congruence-on-x
 (implies
      (natoption/natoptionlist-equiv x x-equiv)
      (equal (natoption/natoptionlist-list->get$inline x)
             (natoption/natoptionlist-list->get$inline x-equiv)))
 :rule-classes :congruence)

Theorem: natoption/natoptionlist-list->get-when-wrong-kind

(defthm natoption/natoptionlist-list->get-when-wrong-kind
  (implies (not (equal (natoption/natoptionlist-kind x)
                       :list))
           (equal (natoption/natoptionlist-list->get x)
                  (nat-option-list-fix nil))))