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• Representation-of-integers

Ulong

Fixtype of values of type unsigned long.

Definitions and Theorems

Function: ulong-equiv$inline

(defun ulong-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (ulongp acl2::x)
                              (ulongp acl2::y))))
  (equal (ulong-fix acl2::x)
         (ulong-fix acl2::y)))

Theorem: ulong-equiv-is-an-equivalence

(defthm ulong-equiv-is-an-equivalence
  (and (booleanp (ulong-equiv x y))
       (ulong-equiv x x)
       (implies (ulong-equiv x y)
                (ulong-equiv y x))
       (implies (and (ulong-equiv x y)
                     (ulong-equiv y z))
                (ulong-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ulong-equiv-implies-equal-ulong-fix-1

(defthm ulong-equiv-implies-equal-ulong-fix-1
  (implies (ulong-equiv acl2::x x-equiv)
           (equal (ulong-fix acl2::x)
                  (ulong-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ulong-fix-under-ulong-equiv

(defthm ulong-fix-under-ulong-equiv
  (ulong-equiv (ulong-fix acl2::x)
               acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))