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Representation-of-integers

Sshort

Fixtype of values of type signed short.

Definitions and Theorems

Function: sshort-equiv$inline

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

Theorem: sshort-equiv-is-an-equivalence

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

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

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

Theorem: sshort-fix-under-sshort-equiv

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