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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:37_1_1"/><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="metric_6.html#T10" target="_self">Th10</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E4:37_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="metric_6.html#E3:37_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="normsp_1.html#T27">NORMSP_1:27</a></i>;<br/>

<b>hence </b><a NAME="E5:37_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tbsp_1.html#V2">convergent</a>
 <b>by </b><i><a class="ref" href="metric_6.html#T38" target="_self">Th38</a></i>;<br/>

<b>hence </b><a NAME="E6:37_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tbsp_1.html#V3">Cauchy</a>
 <b>by </b><i><a class="ref" href="tbsp_1.html#T7">TBSP_1:7</a></i>;<br/>

<b>hence </b><a NAME="E7:37_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="metric_6.html#V1" target="_self">bounded</a>
 <b>by </b><i><a class="ref" href="metric_6.html#T44" target="_self">Th44</a></i>;<br/>


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