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Nati-finite

Nati-finite->get

Get the get field from a nati-finite.

Signature
(nati-finite->get x) → get
Arguments: x — Guard (natip x).
Returns: get — Type (natp get).

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

Definitions and Theorems

Function: nati-finite->get$inline

(defun nati-finite->get$inline (x)
  (declare (xargs :guard (natip x)))
  (declare (xargs :guard (equal (nati-kind x) :finite)))
  (let ((__function__ 'nati-finite->get))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (nati-kind x) :finite) x)))
           (nfix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: natp-of-nati-finite->get

(defthm natp-of-nati-finite->get
  (b* ((get (nati-finite->get$inline x)))
    (natp get))
  :rule-classes :rewrite)

Theorem: nati-finite->get$inline-of-nati-fix-x

(defthm nati-finite->get$inline-of-nati-fix-x
  (equal (nati-finite->get$inline (nati-fix x))
         (nati-finite->get$inline x)))

Theorem: nati-finite->get$inline-nati-equiv-congruence-on-x

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

Theorem: nati-finite->get-when-wrong-kind

(defthm nati-finite->get-when-wrong-kind
  (implies (not (equal (nati-kind x) :finite))
           (equal (nati-finite->get x)
                  (nfix nil))))