<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being  <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> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Olive" title="b1">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Olive" title="b2">p2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Olive" title="b1">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Olive" title="b2">p2</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">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">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c3">p2</font></span>)</span> )</span><br/>





<i><font color="Green" title="E12">A1</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> = 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font>
<b>by </b><i><a class="ref" href="euclid_5.html#T7" target="_self" title="EUCLID_5:th.7">Th7</a></i>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<b>by </b><i><a class="ref" href="euclid_5.html#T3" target="_self" title="EUCLID_5:th.3">Th3</a></i>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><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">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">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="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">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="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">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">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<b>by </b><i><a class="ref" href="euclid_5.html#T15" target="_self" title="EUCLID_5:th.15">Th15</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E13">A2</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> = 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <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="c2">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="c3">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="c2">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="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <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="c2">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="c3">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="c2">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="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <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="c2">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="c3">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="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">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="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>

<br/>.= 
<font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_5.html#T8" target="_self" title="EUCLID_5:th.8">Th8</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> = 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><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">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="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">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">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="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">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="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</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">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="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">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="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</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">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="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<b>by </b><i><a class="txt" href="euclid_5.html#E1:18"><i><font color="Green" title="E12">A1</font></i></a></i>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<b>by </b><i><a class="ref" href="euclid_5.html#T15" target="_self" title="EUCLID_5:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">p2</font> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span>
<b>by </b><i><a class="ref" href="euclid_5.html#T3" target="_self" title="EUCLID_5:th.3">Th3</a></i>
<br/>.= 
<font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c3">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid_5.html#T7" target="_self" title="EUCLID_5:th.7">Th7</a></i>
;<br/>
<b>hence </b><a NAME="E4:18"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p1</font> <a href="euclid_5.html#K5" title="EUCLID_5:func.5">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <font color="Maroon" title="c3">p2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="euclid_5.html#E2:18"><i><font color="Green" title="E13">A2</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>
