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<span class="kw">let </span><font color="Maroon" title="c1">r</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">p</font> = <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">w</font> = <span class="p1"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 1 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" onmouseover="rs('euclid/T22')" onmouseout="rh()">EUCLID:22</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">r2</font> = <font color="Maroon" title="c1">r</font> <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" onmouseover="rs('xreal_0/D1')" onmouseout="rh()">XREAL_0:def 1</a></span>;<br/>
<a NAME="E3:10"/>
 <a href="euclid.html#K11" title="EUCLID:func.11">sqr</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><font color="Maroon" title="c4">r2</font></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T55" onmouseover="rs('rvsum_1/T55')" onmouseout="rh()">RVSUM_1:55</a></span>;<br/>
<span class="kw">then </span><span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> = 
 <a href="square_1.html#K3" title="SQUARE_1:func.3">sqrt</a> <font color="Maroon" title="c4">r2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finsop_1.html#T11" onmouseover="rs('finsop_1/T11')" onmouseout="rh()">FINSOP_1:11</a></span>
<br/>.= 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T72" onmouseover="rs('complex1/T72')" onmouseout="rh()">COMPLEX1:72</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:10"/>
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2"><a href="jordan2b.html#K1" title="JORDAN2B:func.1">|[</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="jordan2b.html#K1" title="JORDAN2B:func.1">]|</a></span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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