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