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<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>thus </b><a NAME="E1:35_1_1"/>
( <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p</font></span><a href="toprns_1.html#K5">.|</a></span> implies for <font color="Olive">w</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>  st <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">w</font> holds <br/><font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Olive">w</font></span><a href="euclid.html#K12">.|</a></span> )
 <b>by </b><i><a class="ref" href="toprns_1.html#D6">TOPRNS_1:def 6</a></i>;<br/>

<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<b>assume </b><a NAME="E3:35_1_1"/>
for <font color="Olive">w</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>  st <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">w</font> holds <br/><font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Olive">w</font></span><a href="euclid.html#K12">.|</a></span>
 ;<br/>

<a NAME="E4:35_1_1"/><b>then </b>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12">|.</a><span class="default"><font color="Maroon">y</font></span><a href="euclid.html#K12">.|</a></span>
 
;<br/>
<b>hence </b><a NAME="E5:35_1_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p</font></span><a href="toprns_1.html#K5">.|</a></span>
 <b>by </b><i><a class="ref" href="toprns_1.html#D6">TOPRNS_1:def 6</a></i>;<br/>


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