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<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K3">R^1</a> ;<br/><b>let </b><font color="Maroon">M</font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">x</font>;<br/>



<b>consider </b><font color="Maroon">V</font> being   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> <b> such that </b><br/><a NAME="E2:49"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">V</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font>
 <b>and </b><br/><a NAME="E4:49"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#T8">CONNSP_2:8</a></i>;<br/>
<a NAME="E5:49"/>
<font color="Maroon">x</font> is   <a href="real_1.html#NM1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E7:49"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E8:49"/><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 <b>by </b><i>, , <a class="ref" href="frechet.html#T8">FRECHET:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">N</font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">r</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> as    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">x</font> <b>by </b><i>, <a class="ref" href="rcomp_1.html#D7">RCOMP_1:def 7</a></i>;<br/>
<b>take </b>
<font color="Maroon">N</font>
;<br/>

<b>thus </b><a NAME="E10:49"/>
<font color="Maroon">N</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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