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<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">y</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a> ;<br/>







<a NAME="E1:8"/><i><font color="Green">E40</font></i>: 
 <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="euclid.html#D1">EUCLID:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span> <b>by </b><i><a class="ref" href="euclid.html#T25">EUCLID:25</a></i>;<br/>
<a NAME="E3:8"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">y</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font></span>)</span> <a href="euclid.html#K20">-</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="euclid.html#T54">EUCLID:54</a></i>;<br/>
<a NAME="E4:8"/>
( <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">y</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">y</font></span>)</span> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x</font> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="euclid.html#K18">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, <a class="ref" href="euclid.html#D11">EUCLID:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:8"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">y</font></span>)</span> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font></span>)</span> <a href="rvsum_1.html#K8">-</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rvsum_1.html#K10">*</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="euclid.html#D13">EUCLID:def 13</a></i>;<br/>


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