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<b>let </b><font color="Maroon" title="c1">N</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">seq</font>, <font color="Maroon" title="c3">seq'</font> be   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Maroon" title="c1">N</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c2">seq</font> is <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c3">seq'</font> is <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>
 ;<br/>

<a NAME="E3:49"/>
 <a href="toprns_1.html#K3" title="TOPRNS_1:func.3">-</a> <font color="Maroon" title="c3">seq'</font> is <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>
 
<b>by </b><i><a class="txt" href="toprns_1.html#E2:49"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="toprns_1.html#T45" target="_self" title="TOPRNS_1:th.45">Th45</a></i>;<br/>
<b>hence </b><a NAME="E4:49"/>
<font color="Maroon" title="c2">seq</font> <a href="toprns_1.html#K4" title="TOPRNS_1:func.4">-</a> <font color="Maroon" title="c3">seq'</font> is <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>
 <b>by </b><i><a class="txt" href="toprns_1.html#E1:49"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="toprns_1.html#T41" target="_self" title="TOPRNS_1:th.41">Th41</a></i>;<br/>


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