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<b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="frechet.html#R1" title="FRECHET:pred.1">is_convergent_to</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c2">S</font> <a href="frechet.html#R1" title="FRECHET:pred.1">is_convergent_to</a> <font color="Maroon" title="c4">x2</font> implies <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:27_1_2"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="frechet.html#R1" title="FRECHET:pred.1">is_convergent_to</a> <font color="Maroon" title="c3">x1</font>
 <b>and </b><br/><a NAME="E2:27_1_2"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="frechet.html#R1" title="FRECHET:pred.1">is_convergent_to</a> <font color="Maroon" title="c4">x2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font></span><br/>

<b>consider </b><font color="Maroon" title="c5">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E4:27_1_2"/><i><font color="Green" title="E26">A5</font></i>: 
 <a href="frechet.html#K1" title="FRECHET:func.1">Lim</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>
<a NAME="E5:27_1_2"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="frechet.html#K1" title="FRECHET:func.1">Lim</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="#E1:27_1_2"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="frechet.html#D4" title="FRECHET:def.4">FRECHET:def 4</a></i>;<br/>
<a NAME="E6:27_1_2"/><b>then </b><i><font color="Green" title="E27">A6</font></i>: 
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font>
 
<b>by </b><i><a class="txt" href="#E4:27_1_2"><i><font color="Green" title="E26">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:27_1_2"/>
<font color="Maroon" title="c4">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="#E2:27_1_2"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="#E4:27_1_2"><i><font color="Green" title="E26">A5</font></i></a>, <a class="ref" href="frechet.html#D4" title="FRECHET:def.4">FRECHET:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:27_1_2"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="#E6:27_1_2"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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