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• Address

Address->index

Get the index field from a address.

Signature

(address->index x) → index

Arguments

x — Guard (address-p x).

Returns

index — Type (maybe-natp index).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: address->index$inline

(defun address->index$inline (x)
 (declare (xargs :guard (address-p x)))
 (declare (xargs :guard t))
 (let ((__function__ 'address->index))
   (declare (ignorable __function__))
   (mbe :logic
        (b* ((x (and t x)))
          (acl2::maybe-natp-fix (if (or (atom x)
                                        (not (eq (car x) :address)))
                                    nil
                                  (nth 2 x))))
        :exec
        (if (or (atom x)
                (not (eq (car x) :address)))
            nil
          (nth 2 x)))))

Theorem: maybe-natp-of-address->index

(defthm maybe-natp-of-address->index
  (b* ((index (address->index$inline x)))
    (maybe-natp index))
  :rule-classes (:rewrite :type-prescription))

Theorem: address->index$inline-of-address-fix-x

(defthm address->index$inline-of-address-fix-x
  (equal (address->index$inline (address-fix x))
         (address->index$inline x)))

Theorem: address->index$inline-address-equiv-congruence-on-x

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