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<b>let </b><font color="Maroon">a</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="rcomp_1.html#D4">RCOMP_1:def 4</a><br/>

<b>assume </b><a NAME="E1:3"/>
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a>  <a href="subset_1.html#K1">{}</a> <a href="numbers.html#K1">REAL</a>  &amp; <font color="Maroon">a</font> is <a href="seq_2.html#V4">convergent</a> )
 ;<br/>

<a NAME="E2:3"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E3:3"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">a</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="E4:3"/>
 <a href="seq_2.html#K2">lim</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="subset_1.html#K1">{}</a> <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>


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