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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:82"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="tsep_1.html#K1" target="_self">union</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" target="_self">Th1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E4:82"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="tsep_1.html#E1:82"><i><font color="Green">E56</font></i></a>, <a class="ref" href="tsep_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E5:82"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>assume </b><a NAME="E6:82"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tsep_1.html#R3" target="_self">are_separated</a> 
 ;<br/>

<a NAME="E7:82"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="connsp_1.html#R1">are_separated</a> 
 
<b>by </b><i><a class="ref" href="tsep_1.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E8:82"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i><a class="txt" href="tsep_1.html#E5:82"><i><font color="Green">E57</font></i></a>, <a class="ref" href="connsp_1.html#T5">CONNSP_1:5</a></i>;<br/>
<b>hence </b><a NAME="E9:82"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T11" target="_self">Th11</a></i>;<br/>


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