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Defbyte-standard-instances

Ubyte7

Fixtype of unsigned bytes of size 7.

Definitions and Theorems

Function: ubyte7-equiv$inline

(defun ubyte7-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte7p x) (ubyte7p y))))
  (equal (ubyte7-fix x) (ubyte7-fix y)))

Theorem: ubyte7-equiv-is-an-equivalence

(defthm ubyte7-equiv-is-an-equivalence
  (and (booleanp (ubyte7-equiv x y))
       (ubyte7-equiv x x)
       (implies (ubyte7-equiv x y)
                (ubyte7-equiv y x))
       (implies (and (ubyte7-equiv x y)
                     (ubyte7-equiv y z))
                (ubyte7-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte7-equiv-implies-equal-ubyte7-fix-1

(defthm ubyte7-equiv-implies-equal-ubyte7-fix-1
  (implies (ubyte7-equiv x x-equiv)
           (equal (ubyte7-fix x)
                  (ubyte7-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte7-fix-under-ubyte7-equiv

(defthm ubyte7-fix-under-ubyte7-equiv
  (ubyte7-equiv (ubyte7-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte7-fix-1-forward-to-ubyte7-equiv

(defthm equal-of-ubyte7-fix-1-forward-to-ubyte7-equiv
  (implies (equal (ubyte7-fix x) y)
           (ubyte7-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte7-fix-2-forward-to-ubyte7-equiv

(defthm equal-of-ubyte7-fix-2-forward-to-ubyte7-equiv
  (implies (equal x (ubyte7-fix y))
           (ubyte7-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte7-equiv-of-ubyte7-fix-1-forward

(defthm ubyte7-equiv-of-ubyte7-fix-1-forward
  (implies (ubyte7-equiv (ubyte7-fix x) y)
           (ubyte7-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte7-equiv-of-ubyte7-fix-2-forward

(defthm ubyte7-equiv-of-ubyte7-fix-2-forward
  (implies (ubyte7-equiv x (ubyte7-fix y))
           (ubyte7-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Ubyte7p: Recognizer for ubyte7.
Ubyte7-fix: Fixer for ubyte7.