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Representation-of-integers

Sllong

Fixtype of values of type signed long long.

Definitions and Theorems

Function: sllong-equiv$inline

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

Theorem: sllong-equiv-is-an-equivalence

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

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

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

Theorem: sllong-fix-under-sllong-equiv

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