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