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<b>consider </b><font color="Maroon">x</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E2:40_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="frechet.html#K1">Lim</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="frechet2.html#E3"><i><font color="Green">Lemma33</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">x</font>
;<br/>

<a NAME="E3:40_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:40_1_1"/>
<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/>


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