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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#L1">TopStruct</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E2:34"/><i><font color="Green">E28</font></i>: 
 <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E3:34"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="frechet2.html#K3" target="_self">Cl_Seq</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:34"/><i><font color="Green">E29</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="frechet.html#K1">Lim</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="frechet2.html#E2:34"><i><font color="Green">E28</font></i></a>, <a class="ref" href="frechet2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E7:34"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="frechet2.html#E6:34"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E8:34"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T65">RELAT_1:65</a></i>;<br/>
<b>hence </b><a NAME="E9:34"/>
contradiction
 <b>by </b><i><a class="ref" href="normsp_1.html#T17">NORMSP_1:17</a></i>;<br/>


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