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Fixtype of unsigned bytes of size 8.
Function:
(defun ubyte8-equiv$inline (x y) (declare (xargs :guard (and (ubyte8p x) (ubyte8p y)))) (equal (ubyte8-fix x) (ubyte8-fix y)))
Theorem:
(defthm ubyte8-equiv-is-an-equivalence (and (booleanp (ubyte8-equiv x y)) (ubyte8-equiv x x) (implies (ubyte8-equiv x y) (ubyte8-equiv y x)) (implies (and (ubyte8-equiv x y) (ubyte8-equiv y z)) (ubyte8-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm ubyte8-equiv-implies-equal-ubyte8-fix-1 (implies (ubyte8-equiv x x-equiv) (equal (ubyte8-fix x) (ubyte8-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm ubyte8-fix-under-ubyte8-equiv (ubyte8-equiv (ubyte8-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-ubyte8-fix-1-forward-to-ubyte8-equiv (implies (equal (ubyte8-fix x) y) (ubyte8-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-ubyte8-fix-2-forward-to-ubyte8-equiv (implies (equal x (ubyte8-fix y)) (ubyte8-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm ubyte8-equiv-of-ubyte8-fix-1-forward (implies (ubyte8-equiv (ubyte8-fix x) y) (ubyte8-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm ubyte8-equiv-of-ubyte8-fix-2-forward (implies (ubyte8-equiv x (ubyte8-fix y)) (ubyte8-equiv x y)) :rule-classes :forward-chaining)