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Fixtype of signed bytes of size 64.
Function:
(defun sbyte64-equiv$inline (x y) (declare (xargs :guard (and (sbyte64p x) (sbyte64p y)))) (equal (sbyte64-fix x) (sbyte64-fix y)))
Theorem:
(defthm sbyte64-equiv-is-an-equivalence (and (booleanp (sbyte64-equiv x y)) (sbyte64-equiv x x) (implies (sbyte64-equiv x y) (sbyte64-equiv y x)) (implies (and (sbyte64-equiv x y) (sbyte64-equiv y z)) (sbyte64-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm sbyte64-equiv-implies-equal-sbyte64-fix-1 (implies (sbyte64-equiv x x-equiv) (equal (sbyte64-fix x) (sbyte64-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm sbyte64-fix-under-sbyte64-equiv (sbyte64-equiv (sbyte64-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-sbyte64-fix-1-forward-to-sbyte64-equiv (implies (equal (sbyte64-fix x) y) (sbyte64-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-sbyte64-fix-2-forward-to-sbyte64-equiv (implies (equal x (sbyte64-fix y)) (sbyte64-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm sbyte64-equiv-of-sbyte64-fix-1-forward (implies (sbyte64-equiv (sbyte64-fix x) y) (sbyte64-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm sbyte64-equiv-of-sbyte64-fix-2-forward (implies (sbyte64-equiv x (sbyte64-fix y)) (sbyte64-equiv x y)) :rule-classes :forward-chaining)