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