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<span class="kw">let </span><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 3</span>)</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"> ( <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> &amp; <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> )</span><br/>

<span class="kw">thus </span><span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c2">q</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T29" onmouseover="rs('anproj_8/T29')" onmouseout="rh()">ANPROJ_8:29</a></span>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T30" onmouseover="rs('anproj_8/T30')" onmouseout="rh()">ANPROJ_8:30</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"> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span></span><br/>

<span class="kw">thus </span><span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c3">r</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T30" onmouseover="rs('anproj_8/T30')" onmouseout="rh()">ANPROJ_8:30</a></span>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">q</font>,<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c1">p</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="anproj_8.html#T29" onmouseover="rs('anproj_8/T29')" onmouseout="rh()">ANPROJ_8:29</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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