第 26776 題：有限乘積拓撲

原題與已知條件

完整finite factor topologies、Cartesian carrier與rectangle-union生成責任。操作=product-topology-boundary；資料={"mode":"nonrectangle_open","model":{"x_points":[0,1],"x_topology":[[],[0],[1],[0,1]],"y_points":[100,101],"y_topology":[[],[100],[101],[100,101]],"candidate_open":[[0,100],[1,101]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整finite factor topologies、Cartesian carrier與rectangle-union生成責任。操作=product-topology-boundary；資料={"mode":"nonrectangle_open","model":{"x_points":[0,1],"x_topology":[[],[0],[1],[0,1]],"y_points":[100,101],"y_topology":[[],[100],[101],[100,101]],"candidate_open":[[0,100],[1,101]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-finite-product-topology

逐步推導

source roles = [product-topology-boundary]

derived = [[mode, points, candidate_open, open, rectangle, rectangles, certificate]]

source roles = [product ORIGINAL X, [0, 1], [[], [0], [1], [0, 1]], 否]

derived = [[0, 1], [[], [0, 1], [0], [1]], [[0, 0, 0, 0, 是, 是], [0, 1, 3, 0, 是, 是], [0, 2, 1, 0, 是, 是], [0, 3, 2, 0, 是, 是], [1, 0, 3, 0, 是, 是], [1, 1, 3, 3, 是, 是], [1, 2, 3, 1, 是, 是], [1, 3, 3, 2, 是, 是], [2, 0, 1, 0, 是, 是], [2, 1, 3, 1, 是, 是], [2, 2, 1, 1, 是, 是], [2, 3, 3, 0, 是, 是], [3, 0, 2, 0, 是, 是], [3, 1, 3, 2, 是, 是], [3, 2, 3, 0, 是, 是], [3, 3, 2, 2, 是, 是]]]

source roles = [product ORIGINAL Y, [100, 101], [[], [100], [101], [100, 101]], 否]

derived = [[100, 101], [[], [100, 101], [100], [101]], [[0, 0, 0, 0, 是, 是], [0, 1, 3, 0, 是, 是], [0, 2, 1, 0, 是, 是], [0, 3, 2, 0, 是, 是], [1, 0, 3, 0, 是, 是], [1, 1, 3, 3, 是, 是], [1, 2, 3, 1, 是, 是], [1, 3, 3, 2, 是, 是], [2, 0, 1, 0, 是, 是], [2, 1, 3, 1, 是, 是], [2, 2, 1, 1, 是, 是], [2, 3, 3, 0, 是, 是], [3, 0, 2, 0, 是, 是], [3, 1, 3, 2, 是, 是], [3, 2, 3, 0, 是, 是], [3, 3, 2, 2, 是, 是]]]

source roles = [[0, 1], [[], [0, 1], [0], [1]], [100, 101], [[], [100, 101], [100], [101]]]

derived = [[[0, 100], [0, 101], [1, 100], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []]]

source roles = [0, [[0, 100], [0, 101], [1, 100], [1, 101]], [[]]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], []]]

source roles = [1, [[0, 100], [0, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101]], []]]

source roles = [2, [[0, 100], [1, 100]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], []]]

source roles = [3, [[0, 100]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], []]]

source roles = [4, [[0, 101], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], []]]

source roles = [5, [[0, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], [[0, 101]], []]]

source roles = [6, [[1, 100], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], [[0, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], []]]

source roles = [7, [[1, 100]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], []]]

source roles = [8, [[1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []]]

source roles = [9, [], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []]]

derived = [[[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []]]

source roles = [product GENERATED all-union topology, [[0, 100], [0, 101], [1, 100], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []], 是]

derived = [[[0, 100], [0, 101], [1, 100], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []], [[0, 0, 15, 15, 是, 是], [0, 1, 15, 7, 是, 是], [0, 2, 15, 11, 是, 是], [0, 3, 15, 3, 是, 是], [0, 4, 15, 13, 是, 是], [0, 5, 15, 5, 是, 是], [0, 6, 15, 9, 是, 是], [0, 7, 15, 1, 是, 是], [0, 8, 15, 14, 是, 是], [0, 9, 15, 6, 是, 是], [0, 10, 15, 10, 是, 是], [0, 11, 15, 2, 是, 是], [0, 12, 15, 12, 是, 是], [0, 13, 15, 4, 是, 是], [0, 14, 15, 8, 是, 是], [0, 15, 15, 0, 是, 是], [1, 0, 15, 7, 是, 是], [1, 1, 7, 7, 是, 是], [1, 2, 15, 3, 是, 是], [1, 3, 7, 3, 是, 是], [1, 4, 15, 5, 是, 是], [1, 5, 7, 5, 是, 是], [1, 6, 15, 1, 是, 是], [1, 7, 7, 1, 是, 是], [1, 8, 15, 6, 是, 是], [1, 9, 7, 6, 是, 是], [1, 10, 15, 2, 是, 是], [1, 11, 7, 2, 是, 是], [1, 12, 15, 4, 是, 是], [1, 13, 7, 4, 是, 是], [1, 14, 15, 0, 是, 是], [1, 15, 7, 0, 是, 是], [2, 0, 15, 11, 是, 是], [2, 1, 15, 3, 是, 是], [2, 2, 11, 11, 是, 是], [2, 3, 11, 3, 是, 是], [2, 4, 15, 9, 是, 是], [2, 5, 15, 1, 是, 是], [2, 6, 11, 9, 是, 是], [2, 7, 11, 1, 是, 是], [2, 8, 15, 10, 是, 是], [2, 9, 15, 2, 是, 是], [2, 10, 11, 10, 是, 是], [2, 11, 11, 2, 是, 是], [2, 12, 15, 8, 是, 是], [2, 13, 15, 0, 是, 是], [2, 14, 11, 8, 是, 是], [2, 15, 11, 0, 是, 是], [3, 0, 15, 3, 是, 是], [3, 1, 7, 3, 是, 是], [3, 2, 11, 3, 是, 是], [3, 3, 3, 3, 是, 是], [3, 4, 15, 1, 是, 是], [3, 5, 7, 1, 是, 是], [3, 6, 11, 1, 是, 是], [3, 7, 3, 1, 是, 是], [3, 8, 15, 2, 是, 是], [3, 9, 7, 2, 是, 是], [3, 10, 11, 2, 是, 是], [3, 11, 3, 2, 是, 是], [3, 12, 15, 0, 是, 是], [3, 13, 7, 0, 是, 是], [3, 14, 11, 0, 是, 是], [3, 15, 3, 0, 是, 是], [4, 0, 15, 13, 是, 是], [4, 1, 15, 5, 是, 是], [4, 2, 15, 9, 是, 是], [4, 3, 15, 1, 是, 是], [4, 4, 13, 13, 是, 是], [4, 5, 13, 5, 是, 是], [4, 6, 13, 9, 是, 是], [4, 7, 13, 1, 是, 是], [4, 8, 15, 12, 是, 是], [4, 9, 15, 4, 是, 是], [4, 10, 15, 8, 是, 是], [4, 11, 15, 0, 是, 是], [4, 12, 13, 12, 是, 是], [4, 13, 13, 4, 是, 是], [4, 14, 13, 8, 是, 是], [4, 15, 13, 0, 是, 是], [5, 0, 15, 5, 是, 是], [5, 1, 7, 5, 是, 是], [5, 2, 15, 1, 是, 是], [5, 3, 7, 1, 是, 是], [5, 4, 13, 5, 是, 是], [5, 5, 5, 5, 是, 是], [5, 6, 13, 1, 是, 是], [5, 7, 5, 1, 是, 是], [5, 8, 15, 4, 是, 是], [5, 9, 7, 4, 是, 是], [5, 10, 15, 0, 是, 是], [5, 11, 7, 0, 是, 是], [5, 12, 13, 4, 是, 是], [5, 13, 5, 4, 是, 是], [5, 14, 13, 0, 是, 是], [5, 15, 5, 0, 是, 是], [6, 0, 15, 9, 是, 是], [6, 1, 15, 1, 是, 是], [6, 2, 11, 9, 是, 是], [6, 3, 11, 1, 是, 是], [6, 4, 13, 9, 是, 是], [6, 5, 13, 1, 是, 是], [6, 6, 9, 9, 是, 是], [6, 7, 9, 1, 是, 是], [6, 8, 15, 8, 是, 是], [6, 9, 15, 0, 是, 是], [6, 10, 11, 8, 是, 是], [6, 11, 11, 0, 是, 是], [6, 12, 13, 8, 是, 是], [6, 13, 13, 0, 是, 是], [6, 14, 9, 8, 是, 是], [6, 15, 9, 0, 是, 是], [7, 0, 15, 1, 是, 是], [7, 1, 7, 1, 是, 是], [7, 2, 11, 1, 是, 是], [7, 3, 3, 1, 是, 是], [7, 4, 13, 1, 是, 是], [7, 5, 5, 1, 是, 是], [7, 6, 9, 1, 是, 是], [7, 7, 1, 1, 是, 是], [7, 8, 15, 0, 是, 是], [7, 9, 7, 0, 是, 是], [7, 10, 11, 0, 是, 是], [7, 11, 3, 0, 是, 是], [7, 12, 13, 0, 是, 是], [7, 13, 5, 0, 是, 是], [7, 14, 9, 0, 是, 是], [7, 15, 1, 0, 是, 是], [8, 0, 15, 14, 是, 是], [8, 1, 15, 6, 是, 是], [8, 2, 15, 10, 是, 是], [8, 3, 15, 2, 是, 是], [8, 4, 15, 12, 是, 是], [8, 5, 15, 4, 是, 是], [8, 6, 15, 8, 是, 是], [8, 7, 15, 0, 是, 是], [8, 8, 14, 14, 是, 是], [8, 9, 14, 6, 是, 是], [8, 10, 14, 10, 是, 是], [8, 11, 14, 2, 是, 是], [8, 12, 14, 12, 是, 是], [8, 13, 14, 4, 是, 是], [8, 14, 14, 8, 是, 是], [8, 15, 14, 0, 是, 是], [9, 0, 15, 6, 是, 是], [9, 1, 7, 6, 是, 是], [9, 2, 15, 2, 是, 是], [9, 3, 7, 2, 是, 是], [9, 4, 15, 4, 是, 是], [9, 5, 7, 4, 是, 是], [9, 6, 15, 0, 是, 是], [9, 7, 7, 0, 是, 是], [9, 8, 14, 6, 是, 是], [9, 9, 6, 6, 是, 是], [9, 10, 14, 2, 是, 是], [9, 11, 6, 2, 是, 是], [9, 12, 14, 4, 是, 是], [9, 13, 6, 4, 是, 是], [9, 14, 14, 0, 是, 是], [9, 15, 6, 0, 是, 是], [10, 0, 15, 10, 是, 是], [10, 1, 15, 2, 是, 是], [10, 2, 11, 10, 是, 是], [10, 3, 11, 2, 是, 是], [10, 4, 15, 8, 是, 是], [10, 5, 15, 0, 是, 是], [10, 6, 11, 8, 是, 是], [10, 7, 11, 0, 是, 是], [10, 8, 14, 10, 是, 是], [10, 9, 14, 2, 是, 是], [10, 10, 10, 10, 是, 是], [10, 11, 10, 2, 是, 是], [10, 12, 14, 8, 是, 是], [10, 13, 14, 0, 是, 是], [10, 14, 10, 8, 是, 是], [10, 15, 10, 0, 是, 是], [11, 0, 15, 2, 是, 是], [11, 1, 7, 2, 是, 是], [11, 2, 11, 2, 是, 是], [11, 3, 3, 2, 是, 是], [11, 4, 15, 0, 是, 是], [11, 5, 7, 0, 是, 是], [11, 6, 11, 0, 是, 是], [11, 7, 3, 0, 是, 是], [11, 8, 14, 2, 是, 是], [11, 9, 6, 2, 是, 是], [11, 10, 10, 2, 是, 是], [11, 11, 2, 2, 是, 是], [11, 12, 14, 0, 是, 是], [11, 13, 6, 0, 是, 是], [11, 14, 10, 0, 是, 是], [11, 15, 2, 0, 是, 是], [12, 0, 15, 12, 是, 是], [12, 1, 15, 4, 是, 是], [12, 2, 15, 8, 是, 是], [12, 3, 15, 0, 是, 是], [12, 4, 13, 12, 是, 是], [12, 5, 13, 4, 是, 是], [12, 6, 13, 8, 是, 是], [12, 7, 13, 0, 是, 是], [12, 8, 14, 12, 是, 是], [12, 9, 14, 4, 是, 是], [12, 10, 14, 8, 是, 是], [12, 11, 14, 0, 是, 是], [12, 12, 12, 12, 是, 是], [12, 13, 12, 4, 是, 是], [12, 14, 12, 8, 是, 是], [12, 15, 12, 0, 是, 是], [13, 0, 15, 4, 是, 是], [13, 1, 7, 4, 是, 是], [13, 2, 15, 0, 是, 是], [13, 3, 7, 0, 是, 是], [13, 4, 13, 4, 是, 是], [13, 5, 5, 4, 是, 是], [13, 6, 13, 0, 是, 是], [13, 7, 5, 0, 是, 是], [13, 8, 14, 4, 是, 是], [13, 9, 6, 4, 是, 是], [13, 10, 14, 0, 是, 是], [13, 11, 6, 0, 是, 是], [13, 12, 12, 4, 是, 是], [13, 13, 4, 4, 是, 是], [13, 14, 12, 0, 是, 是], [13, 15, 4, 0, 是, 是], [14, 0, 15, 8, 是, 是], [14, 1, 15, 0, 是, 是], [14, 2, 11, 8, 是, 是], [14, 3, 11, 0, 是, 是], [14, 4, 13, 8, 是, 是], [14, 5, 13, 0, 是, 是], [14, 6, 9, 8, 是, 是], [14, 7, 9, 0, 是, 是], [14, 8, 14, 8, 是, 是], [14, 9, 14, 0, 是, 是], [14, 10, 10, 8, 是, 是], [14, 11, 10, 0, 是, 是], [14, 12, 12, 8, 是, 是], [14, 13, 12, 0, 是, 是], [14, 14, 8, 8, 是, 是], [14, 15, 8, 0, 是, 是], [15, 0, 15, 0, 是, 是], [15, 1, 7, 0, 是, 是], [15, 2, 11, 0, 是, 是], [15, 3, 3, 0, 是, 是], [15, 4, 13, 0, 是, 是], [15, 5, 5, 0, 是, 是], [15, 6, 9, 0, 是, 是], [15, 7, 1, 0, 是, 是], [15, 8, 14, 0, 是, 是], [15, 9, 6, 0, 是, 是], [15, 10, 10, 0, 是, 是], [15, 11, 2, 0, 是, 是], [15, 12, 12, 0, 是, 是], [15, 13, 4, 0, 是, 是], [15, 14, 8, 0, 是, 是], [15, 15, 0, 0, 是, 是]]]

source roles = [[[0, 100], [1, 101]], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101], [1, 100]], [[0, 100], [0, 101], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100], [1, 101]], [[0, 100], [1, 100]], [[0, 100], [1, 101]], [[0, 100]], [[0, 101], [1, 100], [1, 101]], [[0, 101], [1, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []], [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []]]

derived = [是, 否]

逐步反向核對

• S016 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S015 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S014 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S013 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S012 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S011 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S010 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S009 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S008 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S007 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S006 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S005 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S004 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S003 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S002 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。
• S001 · premise_and_result_audit — 反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。

結論

(nonrectangle_open, [[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [1, 101]], 是, 否, [[[0, 100], [0, 101], [1, 100], [1, 101]], [[0, 100], [0, 101]], [[0, 100], [1, 100]], [[0, 100]], [[0, 101], [1, 101]], [[0, 101]], [[1, 100], [1, 101]], [[1, 100]], [[1, 101]], []], open_union_of_rectangles_need_not_be_one_rectangle)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。