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Uid->uid

Get the uid field from a uid.

Signature
(uid->uid x) → uid
Arguments: x — Guard (uidp x).
Returns: uid — Type (natp uid).

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

Definitions and Theorems

Function: uid->uid$inline

(defun uid->uid$inline (x)
  (declare (xargs :guard (uidp x)))
  (declare (xargs :guard t))
  (mbe :logic (b* ((x (and t x))) (nfix x))
       :exec x))

Theorem: natp-of-uid->uid

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

Theorem: uid->uid$inline-of-uid-fix-x

(defthm uid->uid$inline-of-uid-fix-x
  (equal (uid->uid$inline (uid-fix x))
         (uid->uid$inline x)))

Theorem: uid->uid$inline-uid-equiv-congruence-on-x

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