Basic equivalence relation for maybe-byte-list20 structures.

**Function: **

(defun maybe-byte-list20-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (maybe-byte-list20p acl2::x) (maybe-byte-list20p acl2::y)))) (equal (maybe-byte-list20-fix acl2::x) (maybe-byte-list20-fix acl2::y)))

**Theorem: **

(defthm maybe-byte-list20-equiv-is-an-equivalence (and (booleanp (maybe-byte-list20-equiv x y)) (maybe-byte-list20-equiv x x) (implies (maybe-byte-list20-equiv x y) (maybe-byte-list20-equiv y x)) (implies (and (maybe-byte-list20-equiv x y) (maybe-byte-list20-equiv y z)) (maybe-byte-list20-equiv x z))) :rule-classes (:equivalence))

**Theorem: **

(defthm maybe-byte-list20-equiv-implies-equal-maybe-byte-list20-fix-1 (implies (maybe-byte-list20-equiv acl2::x x-equiv) (equal (maybe-byte-list20-fix acl2::x) (maybe-byte-list20-fix x-equiv))) :rule-classes (:congruence))

**Theorem: **

(defthm maybe-byte-list20-fix-under-maybe-byte-list20-equiv (maybe-byte-list20-equiv (maybe-byte-list20-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))

**Theorem: **

(defthm equal-of-maybe-byte-list20-fix-1-forward-to-maybe-byte-list20-equiv (implies (equal (maybe-byte-list20-fix acl2::x) acl2::y) (maybe-byte-list20-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)

**Theorem: **

(defthm equal-of-maybe-byte-list20-fix-2-forward-to-maybe-byte-list20-equiv (implies (equal acl2::x (maybe-byte-list20-fix acl2::y)) (maybe-byte-list20-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)

**Theorem: **

(defthm maybe-byte-list20-equiv-of-maybe-byte-list20-fix-1-forward (implies (maybe-byte-list20-equiv (maybe-byte-list20-fix acl2::x) acl2::y) (maybe-byte-list20-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)

**Theorem: **

(defthm maybe-byte-list20-equiv-of-maybe-byte-list20-fix-2-forward (implies (maybe-byte-list20-equiv acl2::x (maybe-byte-list20-fix acl2::y)) (maybe-byte-list20-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)