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Representation-of-integers

Ushort

Fixtype of values of type unsigned short.

Definitions and Theorems

Function: ushort-equiv$inline

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

Theorem: ushort-equiv-is-an-equivalence

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

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

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

Theorem: ushort-fix-under-ushort-equiv

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