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Defbyte-standard-instances

Ubyte11

Fixtype of unsigned bytes of size 11.

Definitions and Theorems

Function: ubyte11-equiv$inline

(defun ubyte11-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte11p x) (ubyte11p y))))
  (equal (ubyte11-fix x) (ubyte11-fix y)))

Theorem: ubyte11-equiv-is-an-equivalence

(defthm ubyte11-equiv-is-an-equivalence
  (and (booleanp (ubyte11-equiv x y))
       (ubyte11-equiv x x)
       (implies (ubyte11-equiv x y)
                (ubyte11-equiv y x))
       (implies (and (ubyte11-equiv x y)
                     (ubyte11-equiv y z))
                (ubyte11-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte11-equiv-implies-equal-ubyte11-fix-1

(defthm ubyte11-equiv-implies-equal-ubyte11-fix-1
  (implies (ubyte11-equiv x x-equiv)
           (equal (ubyte11-fix x)
                  (ubyte11-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte11-fix-under-ubyte11-equiv

(defthm ubyte11-fix-under-ubyte11-equiv
  (ubyte11-equiv (ubyte11-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte11-fix-1-forward-to-ubyte11-equiv

(defthm equal-of-ubyte11-fix-1-forward-to-ubyte11-equiv
  (implies (equal (ubyte11-fix x) y)
           (ubyte11-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte11-fix-2-forward-to-ubyte11-equiv

(defthm equal-of-ubyte11-fix-2-forward-to-ubyte11-equiv
  (implies (equal x (ubyte11-fix y))
           (ubyte11-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte11-equiv-of-ubyte11-fix-1-forward

(defthm ubyte11-equiv-of-ubyte11-fix-1-forward
  (implies (ubyte11-equiv (ubyte11-fix x) y)
           (ubyte11-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte11-equiv-of-ubyte11-fix-2-forward

(defthm ubyte11-equiv-of-ubyte11-fix-2-forward
  (implies (ubyte11-equiv x (ubyte11-fix y))
           (ubyte11-equiv x y))
  :rule-classes :forward-chaining)

Subtopics

Ubyte11s-as-digits-in-base-2048: Specialized versions of the operations to convert between natural numbers and digits that use unsigned 11-bit bytes as digits, in base 2048.
Ubyte11p: Recognizer for ubyte11.
Ubyte11-fix: Fixer for ubyte11.