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