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