		Search-engine friendly clone of the ACL2 documentation.

Defbyte-standard-instances

Sbyte3

Fixtype of signed bytes of size 3.

Definitions and Theorems

Function: sbyte3-equiv$inline

(defun sbyte3-equiv$inline (x y)
  (declare (xargs :guard (and (sbyte3p x) (sbyte3p y))))
  (equal (sbyte3-fix x) (sbyte3-fix y)))

Theorem: sbyte3-equiv-is-an-equivalence

(defthm sbyte3-equiv-is-an-equivalence
  (and (booleanp (sbyte3-equiv x y))
       (sbyte3-equiv x x)
       (implies (sbyte3-equiv x y)
                (sbyte3-equiv y x))
       (implies (and (sbyte3-equiv x y)
                     (sbyte3-equiv y z))
                (sbyte3-equiv x z)))
  :rule-classes (:equivalence))

Theorem: sbyte3-equiv-implies-equal-sbyte3-fix-1

(defthm sbyte3-equiv-implies-equal-sbyte3-fix-1
  (implies (sbyte3-equiv x x-equiv)
           (equal (sbyte3-fix x)
                  (sbyte3-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: sbyte3-fix-under-sbyte3-equiv

(defthm sbyte3-fix-under-sbyte3-equiv
  (sbyte3-equiv (sbyte3-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-sbyte3-fix-1-forward-to-sbyte3-equiv

(defthm equal-of-sbyte3-fix-1-forward-to-sbyte3-equiv
  (implies (equal (sbyte3-fix x) y)
           (sbyte3-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-sbyte3-fix-2-forward-to-sbyte3-equiv

(defthm equal-of-sbyte3-fix-2-forward-to-sbyte3-equiv
  (implies (equal x (sbyte3-fix y))
           (sbyte3-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte3-equiv-of-sbyte3-fix-1-forward

(defthm sbyte3-equiv-of-sbyte3-fix-1-forward
  (implies (sbyte3-equiv (sbyte3-fix x) y)
           (sbyte3-equiv x y))
  :rule-classes :forward-chaining)

Theorem: sbyte3-equiv-of-sbyte3-fix-2-forward

(defthm sbyte3-equiv-of-sbyte3-fix-2-forward
  (implies (sbyte3-equiv x (sbyte3-fix y))
           (sbyte3-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Sbyte3p: Recognizer for sbyte3.
Sbyte3-fix: Fixer for sbyte3.