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<b>let </b><font color="Maroon">T</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">S</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:24"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">S</font> is <a href="frechet.html#V2">convergent</a>
 ;<br/>

<b>assume </b><a NAME="E2:24"/><i><font color="Green">E31</font></i>: 
 <a href="frechet.html#K1">Lim</a> <font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="frechet.html#K1">Lim</a> <font color="Maroon">S</font>;<br/>
<a NAME="E4:24"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="frechet.html#K1">Lim</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E6:24"/>
<font color="Maroon">S</font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="frechet.html#D4">FRECHET:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:24"/>
contradiction
 <b>by </b><i>, <a class="ref" href="frechet.html#D3">FRECHET:def 3</a></i>;<br/>


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