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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>





<b>assume </b><a NAME="E1:21"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>7</sub></font> is <a href="connsp_1.html#V1">connected</a> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>8</sub></font> is <a href="connsp_1.html#V1">connected</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_1.html#D3">CONNSP_1:def 3</a><br/>

<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>8</sub></font> as  <a href="connsp_1.html#V1">connected</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/>
<a NAME="E3:21"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> is <a href="connsp_1.html#V1">connected</a>
 
;<br/>
<b>hence </b><a NAME="E4:21"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="pre_topc.html#K3">|</a> <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="borsuk_1.html#K6">:]</a></span> is <a href="connsp_1.html#V1">connected</a>
 <b>by </b><i><a class="ref" href="borsuk_3.html#T26">BORSUK_3:26</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="connsp_1.html#D3">CONNSP_1:def 3</a><br/>


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