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Representation-of-integers

Sint

Fixtype of values of type signed int.

Definitions and Theorems

Function: sint-equiv$inline

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

Theorem: sint-equiv-is-an-equivalence

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

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

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

Theorem: sint-fix-under-sint-equiv

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