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Address

Address->number

Get the number field from a address.

Signature
(address->number x) → number
Arguments: x — Guard (addressp x).
Returns: number — Type (natp number).

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

Definitions and Theorems

Function: address->number$inline

(defun address->number$inline (x)
  (declare (xargs :guard (addressp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'address->number))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: natp-of-address->number

(defthm natp-of-address->number
  (b* ((number (address->number$inline x)))
    (natp number))
  :rule-classes :rewrite)

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

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

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

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