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Representation-of-integers

Slong

Fixtype of values of type signed long.

Definitions and Theorems

Function: slong-equiv$inline

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

Theorem: slong-equiv-is-an-equivalence

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

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

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

Theorem: slong-fix-under-slong-equiv

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