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• Fty::basetypes
• Maybe-natp

Maybe-natp-fix

(maybe-natp-fix x) is the identity for maybe-natps, or coerces any invalid object to nil.

Performance note. In the execution this is just an inlined identity function, i.e., it should have zero runtime cost.

Definitions and Theorems

Function: maybe-natp-fix$inline

(defun maybe-natp-fix$inline (x)
  (declare (xargs :guard (maybe-natp x)))
  (mbe :logic (if x (nfix x) nil)
       :exec x))

Theorem: maybe-natp-of-maybe-natp-fix

(defthm maybe-natp-of-maybe-natp-fix
  (maybe-natp (maybe-natp-fix x))
  :rule-classes (:rewrite :type-prescription))

Theorem: maybe-natp-fix-when-maybe-natp

(defthm maybe-natp-fix-when-maybe-natp
  (implies (maybe-natp x)
           (equal (maybe-natp-fix x) x)))

Theorem: maybe-natp-fix-under-iff

(defthm maybe-natp-fix-under-iff
  (iff (maybe-natp-fix x) x))

Theorem: maybe-natp-fix-under-nat-equiv

(defthm maybe-natp-fix-under-nat-equiv
  (nat-equiv (maybe-natp-fix x) x))