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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>,   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>) <b>-&gt; </b>  <a href="real_1.html#NM1">Real</a> = <span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="euclid.html#K8" target="_self">-</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E2:33_1_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font> holds  <font color="Maroon">f</font> <a href="metric_1.html#K1">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>,<font color="Olive">y</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>, <font color="Maroon">y</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1" target="_self">REAL</a> <font color="Maroon">n</font>;<br/>

<b>thus </b><a NAME="E3:33_1_1"/>
<font color="Maroon">f</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K12" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K8" target="_self">-</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid.html#K12" target="_self">.|</a></span>
 <b>by </b><i/>;<br/>


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