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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:121"/><i><font color="Green">E93</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="borsuk_5.html#V1" target="_self">with_proper_subsets</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:121"/>
not <font color="Maroon">c<sub>3</sub></font> is <a href="borsuk_5.html#V1" target="_self">with_proper_subsets</a>
 ;<br/>

<a NAME="E3:121"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:121"/>
contradiction
 <b>by </b><i><a class="txt" href="borsuk_5.html#E1:121"><i><font color="Green">E93</font></i></a>, <a class="ref" href="borsuk_5.html#D6" target="_self">Def6</a></i>;<br/>


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