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<span class="kw">let </span><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</font>, <font color="Maroon" title="c3">p3</font> be    <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> 3; <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">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span></span><br/>





<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font> = 
 <a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_8.html#T83" target="_self" onmouseover="rs('euclid_8/T83')" onmouseout="rh()">Th74</a></span>
<br/>.= 
 <a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_8.html#T86" target="_self" onmouseover="rs('euclid_8/T86')" onmouseout="rh()">Th77</a></span>
<br/>.= 
 <a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c1">p1</font></span>)</span> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_8.html#T83" target="_self" onmouseover="rs('euclid_8/T83')" onmouseout="rh()">Th74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K6" title="EUCLID:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p3</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c1">p1</font></span>)</span></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T36" onmouseover="rs('rvsum_1/T36')" onmouseout="rh()">RVSUM_1:36</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:90"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_8.html#K5" title="EUCLID_8:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_8.html#T83" target="_self" onmouseover="rs('euclid_8/T83')" onmouseout="rh()">Th74</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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