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<b>let </b><font color="Maroon">TS</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="borsuk_5.html#V1" target="_self">with_proper_subsets</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">TS</font>, <font color="Maroon">B</font> be  <a href="borsuk_5.html#V1" target="_self">with_proper_subsets</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">TS</font>;<br/>



<b>assume </b><a NAME="E1:123"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">TS</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_5.html#D6" target="_self">BORSUK_5:def 6</a><br/>

<a NAME="E2:123"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">TS</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">TS</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:123"/>
contradiction
 <b>by </b><i/>;<br/>


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