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<b>let </b><font color="Maroon" title="c1">p1</font>, <font color="Maroon" title="c2">p2</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">p1</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>



<i><font color="Green" title="E19">A1</font></i>: <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_5.html#T29" target="_self" title="EUCLID_5:th.29">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>
<span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</font></span><a href="euclid_5.html#K6" title="EUCLID_5:func.6">}|</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid_5.html#T29" target="_self" title="EUCLID_5:th.29">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c2">p2</font></span>)</span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span>

;<br/>
<b>hence </b><a NAME="E3:33"/>
( <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1"><a href="euclid_5.html#K6" title="EUCLID_5:func.6">|{</a><span class="default"><font color="Maroon" title="c2">p2</font>,<font color="Maroon" title="c1">p1</font>,<font color="Maroon" title="c2">p2</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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="euclid_5.html#E1:33"><i><font color="Green" title="E19">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
