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<b>let </b><font color="Maroon" title="c1">TS</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">TS</font>;<br/>



<b>assume </b><a NAME="E1:119"/><i><font color="Green" title="E78">A1</font></i>: 
( <font color="Maroon" title="c2">F</font> is <a href="borsuk_5.html#V1" title="BORSUK_5:attr.1">with_proper_subsets</a> &amp; <font color="Maroon" title="c3">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> )
 ;<br/>

<b>assume </b><a NAME="E2:119"/>
not <font color="Maroon" title="c3">G</font> is <a href="borsuk_5.html#V1" title="BORSUK_5:attr.1">with_proper_subsets</a>
 ;<br/>

<a NAME="E3:119"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">TS</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#D6" target="_self" title="BORSUK_5:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:119"/>
contradiction
 <b>by </b><i><a class="txt" href="borsuk_5.html#E1:119"><i><font color="Green" title="E78">A1</font></i></a>, <a class="ref" href="borsuk_5.html#D6" target="_self" title="BORSUK_5:def.6">Def6</a></i>;<br/>


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