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<b>let </b><font color="Maroon">p1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 3</span>)</span>;<br/><b>let </b><font color="Maroon">p2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 3</span>)</span>;<br/><b>let </b><font color="Maroon">p3</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 3</span>)</span>;<br/>





<a NAME="E1:25"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:25"/><b>then </b><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font></span>)</span> <a href="euclid_5.html#K1" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:25"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font></span>)</span> <a href="euclid_5.html#K2" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:25"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font></span>)</span> <a href="euclid_5.html#K3" target="_self">`3</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:25"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
 
<b>by </b><i>, , </i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <font color="Maroon">p2</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <font color="Maroon">p3</font></span>)</span> = 
<span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`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"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`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"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K3" target="_self">`3</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K3" target="_self">`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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">p2</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p5">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K2" target="_self">`2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">p3</font> <a href="euclid_5.html#K1" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span><a href="euclid_5.html#K4" target="_self">]|</a></span>

;<br/>
<b>hence </b><a NAME="E7:25"/>
<font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p2</font> <a href="euclid.html#K17">+</a> <font color="Maroon">p3</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <font color="Maroon">p2</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="euclid_5.html#K5" target="_self">&lt;X&gt;</a> <font color="Maroon">p3</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
