		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integers

Schar

Fixtype of values of type signed char.

Definitions and Theorems

Function: schar-equiv$inline

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

Theorem: schar-equiv-is-an-equivalence

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

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

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

Theorem: schar-fix-under-schar-equiv

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