Basic equivalence relation for tree-list-tuple6-result structures.
Function:
(defun abnf::tree-list-tuple6-result-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (abnf::tree-list-tuple6-resultp acl2::x) (abnf::tree-list-tuple6-resultp acl2::y)))) (equal (abnf::tree-list-tuple6-result-fix acl2::x) (abnf::tree-list-tuple6-result-fix acl2::y)))
Theorem:
(defthm abnf::tree-list-tuple6-result-equiv-is-an-equivalence (and (booleanp (abnf::tree-list-tuple6-result-equiv abnf::x abnf::y)) (abnf::tree-list-tuple6-result-equiv abnf::x abnf::x) (implies (abnf::tree-list-tuple6-result-equiv abnf::x abnf::y) (abnf::tree-list-tuple6-result-equiv abnf::y abnf::x)) (implies (and (abnf::tree-list-tuple6-result-equiv abnf::x abnf::y) (abnf::tree-list-tuple6-result-equiv abnf::y abnf::z)) (abnf::tree-list-tuple6-result-equiv abnf::x abnf::z))) :rule-classes (:equivalence))
Theorem:
(defthm abnf::tree-list-tuple6-result-equiv-implies-equal-tree-list-tuple6-result-fix-1 (implies (abnf::tree-list-tuple6-result-equiv acl2::x abnf::x-equiv) (equal (abnf::tree-list-tuple6-result-fix acl2::x) (abnf::tree-list-tuple6-result-fix abnf::x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm abnf::tree-list-tuple6-result-fix-under-tree-list-tuple6-result-equiv (abnf::tree-list-tuple6-result-equiv (abnf::tree-list-tuple6-result-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm abnf::equal-of-tree-list-tuple6-result-fix-1-forward-to-tree-list-tuple6-result-equiv (implies (equal (abnf::tree-list-tuple6-result-fix acl2::x) acl2::y) (abnf::tree-list-tuple6-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm abnf::equal-of-tree-list-tuple6-result-fix-2-forward-to-tree-list-tuple6-result-equiv (implies (equal acl2::x (abnf::tree-list-tuple6-result-fix acl2::y)) (abnf::tree-list-tuple6-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm abnf::tree-list-tuple6-result-equiv-of-tree-list-tuple6-result-fix-1-forward (implies (abnf::tree-list-tuple6-result-equiv (abnf::tree-list-tuple6-result-fix acl2::x) acl2::y) (abnf::tree-list-tuple6-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm abnf::tree-list-tuple6-result-equiv-of-tree-list-tuple6-result-fix-2-forward (implies (abnf::tree-list-tuple6-result-equiv acl2::x (abnf::tree-list-tuple6-result-fix acl2::y)) (abnf::tree-list-tuple6-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)