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Byte-list64

A fixtype of true lists of (unsigned 8-bit) bytes of length 64.

Definitions and Theorems

Function: byte-list64-equiv$inline

(defun byte-list64-equiv$inline (x y)
       (declare (xargs :guard (and (byte-list64p x)
                                   (byte-list64p y))))
       (equal (byte-list64-fix x)
              (byte-list64-fix y)))

Theorem: byte-list64-equiv-is-an-equivalence

(defthm byte-list64-equiv-is-an-equivalence
        (and (booleanp (byte-list64-equiv x y))
             (byte-list64-equiv x x)
             (implies (byte-list64-equiv x y)
                      (byte-list64-equiv y x))
             (implies (and (byte-list64-equiv x y)
                           (byte-list64-equiv y z))
                      (byte-list64-equiv x z)))
        :rule-classes (:equivalence))

Theorem: byte-list64-equiv-implies-equal-byte-list64-fix-1

(defthm byte-list64-equiv-implies-equal-byte-list64-fix-1
        (implies (byte-list64-equiv x x-equiv)
                 (equal (byte-list64-fix x)
                        (byte-list64-fix x-equiv)))
        :rule-classes (:congruence))

Theorem: byte-list64-fix-under-byte-list64-equiv

(defthm byte-list64-fix-under-byte-list64-equiv
        (byte-list64-equiv (byte-list64-fix x)
                           x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-byte-list64-fix-1-forward-to-byte-list64-equiv

(defthm equal-of-byte-list64-fix-1-forward-to-byte-list64-equiv
        (implies (equal (byte-list64-fix x) y)
                 (byte-list64-equiv x y))
        :rule-classes :forward-chaining)

Theorem: equal-of-byte-list64-fix-2-forward-to-byte-list64-equiv

(defthm equal-of-byte-list64-fix-2-forward-to-byte-list64-equiv
        (implies (equal x (byte-list64-fix y))
                 (byte-list64-equiv x y))
        :rule-classes :forward-chaining)

Theorem: byte-list64-equiv-of-byte-list64-fix-1-forward

(defthm byte-list64-equiv-of-byte-list64-fix-1-forward
        (implies (byte-list64-equiv (byte-list64-fix x)
                                    y)
                 (byte-list64-equiv x y))
        :rule-classes :forward-chaining)

Theorem: byte-list64-equiv-of-byte-list64-fix-2-forward

(defthm byte-list64-equiv-of-byte-list64-fix-2-forward
        (implies (byte-list64-equiv x (byte-list64-fix y))
                 (byte-list64-equiv x y))
        :rule-classes :forward-chaining)

Subtopics

Byte-list64p: Recognizer for byte-list64.
Byte-list64-fix: Fixer for byte-list64.