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Address+pos

Address+pos->address

Get the address field from a address+pos.

Signature
(address+pos->address x) → address
Arguments: x — Guard (address+pos-p x).
Returns: address — Type (addressp address).

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

Definitions and Theorems

Function: address+pos->address$inline

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

Theorem: addressp-of-address+pos->address

(defthm addressp-of-address+pos->address
  (b* ((address (address+pos->address$inline x)))
    (addressp address))
  :rule-classes :rewrite)

Theorem: address+pos->address$inline-of-address+pos-fix-x

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

Theorem: address+pos->address$inline-address+pos-equiv-congruence-on-x

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