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