		Search-engine friendly clone of the ACL2 documentation.

Defbyte-standard-instances

Sbyte128

Fixtype of signed bytes of size 128.

Definitions and Theorems

Function: sbyte128-equiv$inline

(defun sbyte128-equiv$inline (x y)
  (declare (xargs :guard (and (sbyte128p x) (sbyte128p y))))
  (equal (sbyte128-fix x)
         (sbyte128-fix y)))

Theorem: sbyte128-equiv-is-an-equivalence

(defthm sbyte128-equiv-is-an-equivalence
  (and (booleanp (sbyte128-equiv x y))
       (sbyte128-equiv x x)
       (implies (sbyte128-equiv x y)
                (sbyte128-equiv y x))
       (implies (and (sbyte128-equiv x y)
                     (sbyte128-equiv y z))
                (sbyte128-equiv x z)))
  :rule-classes (:equivalence))

Theorem: sbyte128-equiv-implies-equal-sbyte128-fix-1

(defthm sbyte128-equiv-implies-equal-sbyte128-fix-1
  (implies (sbyte128-equiv x x-equiv)
           (equal (sbyte128-fix x)
                  (sbyte128-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: sbyte128-fix-under-sbyte128-equiv

(defthm sbyte128-fix-under-sbyte128-equiv
  (sbyte128-equiv (sbyte128-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-sbyte128-fix-1-forward-to-sbyte128-equiv

(defthm equal-of-sbyte128-fix-1-forward-to-sbyte128-equiv
  (implies (equal (sbyte128-fix x) y)
           (sbyte128-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-sbyte128-fix-2-forward-to-sbyte128-equiv

(defthm equal-of-sbyte128-fix-2-forward-to-sbyte128-equiv
  (implies (equal x (sbyte128-fix y))
           (sbyte128-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte128-equiv-of-sbyte128-fix-1-forward

(defthm sbyte128-equiv-of-sbyte128-fix-1-forward
  (implies (sbyte128-equiv (sbyte128-fix x) y)
           (sbyte128-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte128-equiv-of-sbyte128-fix-2-forward

(defthm sbyte128-equiv-of-sbyte128-fix-2-forward
  (implies (sbyte128-equiv x (sbyte128-fix y))
           (sbyte128-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Sbyte128p: Recognizer for sbyte128.
Sbyte128-fix: Fixer for sbyte128.
Sbyte128-ihs-theorems: Theorems about sbyte128 and IHS functions.