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Representation-of-integers

Uint

Fixtype of values of type unsigned int.

Definitions and Theorems

Function: uint-equiv$inline

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

Theorem: uint-equiv-is-an-equivalence

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

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

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

Theorem: uint-fix-under-uint-equiv

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