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Byte

A fixtype of (unsigned 8-bit) bytes.

We use fty::defbyte to generate this fixtype, along with the recognizer, fixer, and equivalence. The recognizer is identical to bytep.

Definitions and Theorems

Function: byte-equiv$inline

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

Theorem: byte-equiv-is-an-equivalence

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

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

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

Theorem: byte-fix-under-byte-equiv

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

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

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

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

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

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

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

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

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

Subtopics

Byte-list: A fixtype of true lists of (unsigned 8-bit) bytes.
Byte-fix: Fixer for byte.
Bytep-additional-theorems: Additional theorems about byte.