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  "body": "\n## Statement\n\nLet the set $X$ be represented by the points inside the rectangular region in Fig. 5. Also, let $A,B$ be any two non-intersection subsets (*i.e.* subsets spatially far from each other) in $X$, as shown in Fig. 5. Let $C^c = X \\backslash C$ ([[complement|0RKF1ZT5JJ]] of the set $C$). Then from the EF-axiom, observe the following:\n\n$$\\begin{aligned} A \u0026{}\\mathrel{\\underline{\\delta}} B,\\\\ B \u0026\\subset C,\\\\ D \u0026= C^c,\\\\ X \u0026= D \\cup C,\\\\ A \u0026\\subset D,\\ \\mbox{hence, we can write}\\\\ A\\ \\underline{\\delta}\\ B\\ \u0026\\Rightarrow\\ A\\ \\underline{\\delta}\\ C\\ \\mbox{and}\\ B\\ \\underline{\\delta}\\ D,\\ \\mbox{for some}\\ C,D\\ \\mbox{in}\\ X \\mbox{ so that } C\\cup D = X. \\qquad \\blacksquare \\end{aligned}$$\n",
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