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Defbyte-standard-instances

Ubyte2

Fixtype of unsigned bytes of size 2.

Definitions and Theorems

Function: ubyte2-equiv$inline

(defun ubyte2-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte2p x) (ubyte2p y))))
  (equal (ubyte2-fix x) (ubyte2-fix y)))

Theorem: ubyte2-equiv-is-an-equivalence

(defthm ubyte2-equiv-is-an-equivalence
  (and (booleanp (ubyte2-equiv x y))
       (ubyte2-equiv x x)
       (implies (ubyte2-equiv x y)
                (ubyte2-equiv y x))
       (implies (and (ubyte2-equiv x y)
                     (ubyte2-equiv y z))
                (ubyte2-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte2-equiv-implies-equal-ubyte2-fix-1

(defthm ubyte2-equiv-implies-equal-ubyte2-fix-1
  (implies (ubyte2-equiv x x-equiv)
           (equal (ubyte2-fix x)
                  (ubyte2-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte2-fix-under-ubyte2-equiv

(defthm ubyte2-fix-under-ubyte2-equiv
  (ubyte2-equiv (ubyte2-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte2-fix-1-forward-to-ubyte2-equiv

(defthm equal-of-ubyte2-fix-1-forward-to-ubyte2-equiv
  (implies (equal (ubyte2-fix x) y)
           (ubyte2-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte2-fix-2-forward-to-ubyte2-equiv

(defthm equal-of-ubyte2-fix-2-forward-to-ubyte2-equiv
  (implies (equal x (ubyte2-fix y))
           (ubyte2-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte2-equiv-of-ubyte2-fix-1-forward

(defthm ubyte2-equiv-of-ubyte2-fix-1-forward
  (implies (ubyte2-equiv (ubyte2-fix x) y)
           (ubyte2-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte2-equiv-of-ubyte2-fix-2-forward

(defthm ubyte2-equiv-of-ubyte2-fix-2-forward
  (implies (ubyte2-equiv x (ubyte2-fix y))
           (ubyte2-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Ubyte2p: Recognizer for ubyte2.
Ubyte2-fix: Fixer for ubyte2.