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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" target="_self">REAL-NS</a> <font color="Maroon">n</font></span>)</span>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:11"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<b>thus </b><font color="Maroon">a</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="real_ns1.html#K2" target="_self">Euclid_mult</a> <font color="Maroon">n</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a</font> <a href="euclid.html#K9">*</a> <font color="Maroon">y</font>
<b>by </b><i>, </i>
;<br/>


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