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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> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:41"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:41"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>hence </b><a NAME="E3:41"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="compts_1.html#V6">compact</a> implies <font color="Maroon">c<sub>4</sub></font> is <a href="compts_1.html#V6">compact</a> )
 <b>by </b><i><a class="txt" href="borsuk_1.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="ref" href="compts_1.html#T11">COMPTS_1:11</a></i>;<br/>

<b>assume </b><a NAME="E4:41"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="compts_1.html#V6">compact</a>
 ;<br/>

<a NAME="E5:41"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E1:41"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:41"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="txt" href="borsuk_1.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="borsuk_1.html#E2:41"><i><font color="Green">E33</font></i></a>, <a class="ref" href="compts_1.html#T11">COMPTS_1:11</a></i>;<br/>


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