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Nxst-node

Nxst-node->reg

Get the reg field from a nxst-node.

Signature
(nxst-node->reg x) → reg
Arguments: x — Guard (node-p x).
Returns: reg — Type (natp reg).

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

Definitions and Theorems

Function: nxst-node->reg$inline

(defun nxst-node->reg$inline (x)
  (declare (xargs :guard (node-p x)))
  (declare (xargs :guard (equal (stype x) :nxst)))
  (let ((__function__ 'nxst-node->reg))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (stype x) :nxst) x)))
           (nfix (caddr x)))
         :exec (caddr x))))

Theorem: natp-of-nxst-node->reg

(defthm natp-of-nxst-node->reg
  (b* ((reg (nxst-node->reg$inline x)))
    (natp reg))
  :rule-classes :type-prescription)

Theorem: nxst-node->reg$inline-of-node-fix-x

(defthm nxst-node->reg$inline-of-node-fix-x
  (equal (nxst-node->reg$inline (node-fix x))
         (nxst-node->reg$inline x)))

Theorem: nxst-node->reg$inline-node-equiv-congruence-on-x

(defthm nxst-node->reg$inline-node-equiv-congruence-on-x
  (implies (node-equiv x x-equiv)
           (equal (nxst-node->reg$inline x)
                  (nxst-node->reg$inline x-equiv)))
  :rule-classes :congruence)

Theorem: nxst-node->reg-when-wrong-kind

(defthm nxst-node->reg-when-wrong-kind
  (implies (not (equal (stype x) :nxst))
           (equal (nxst-node->reg x) (nfix nil))))