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

<b>let </b><font color="Maroon">X</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green">E48</font></i>: 
 <a href="conmetr.html#NR3" target="_self">MH1_holds_in</a> <font color="Maroon">X</font>
 ;<br/>

<b>assume </b><a NAME="E2:16"/><i><font color="Green">E49</font></i>: 
 <a href="conmetr.html#NR4" target="_self">MH2_holds_in</a> <font color="Maroon">X</font>
 ;<br/>

<b>let </b><font color="Maroon">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D1" target="_self">CONMETR:def 1</a><br/><b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">a3</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">b2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">b3</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>

















<b>assume </b><a NAME="E3:16"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; not <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; not <font color="Maroon">a3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">M</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">N</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">o'</font> = <font color="Maroon">o</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">a2'</font> = <font color="Maroon">a2</font>, <font color="Maroon">a3'</font> = <font color="Maroon">a3</font>, <font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2'</font> = <font color="Maroon">b2</font>, <font color="Maroon">b3'</font> = <font color="Maroon">b3</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">M'</font> = <font color="Maroon">M</font>, <font color="Maroon">N'</font> = <font color="Maroon">N</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/>
<a NAME="E6:16"/>
( <font color="Maroon">M</font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">N</font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<a NAME="E7:16"/><b>then </b><i><font color="Green">E71</font></i>: 
( <font color="Maroon">M'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">N'</font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:16"/><b>then </b><i><font color="Green">E72</font></i>: 
( <font color="Maroon">M'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M'</font> &amp; <font color="Maroon">N'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">N'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<div><i><font color="Green">E73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E74</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> or <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font> or <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font> )
 ;<br/><div><i><font color="Green">E75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font>
 ;<br/><a NAME="E2:16_1_1"/><i><font color="Green">E77</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:16_1_1"/>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_1"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_1_1"/>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_1_1_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_1_1_1"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:16_1_1_1_1"/>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:16_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:16_1_1_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:16_1_1_1"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_1_1"/>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E6:16_1_1"/><b>then </b>
<font color="Maroon">b2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E7:16_1_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E8:16_1_1"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E80</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/><a NAME="E2:16_1_2"/><i><font color="Green">E82</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 ;<br/>

<a NAME="E2:16_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_1_2"/>
<font color="Maroon">o'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_2"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">b2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_1_2"/>
<font color="Maroon">a3</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E6:16_1_2"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E7:16_1_2"/><b>then </b>
<font color="Maroon">a2</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, , , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E8:16_1_2"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_3"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/><a NAME="E2:16_1_3"/><i><font color="Green">E85</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 ;<br/>

<a NAME="E2:16_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1_3_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_1_3"/>
<font color="Maroon">o'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:16_1_3"/><b>then </b><i><font color="Green">E86</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:16_1_3"/>
<font color="Maroon">a3</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E6:16_1_3"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E7:16_1_3"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i>, , , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:16_1"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> )
 ;<br/><a NAME="E2:16_2"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_1"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3</font>
 ;<br/>

<a NAME="E2:16_2_1"/><i><font color="Green">E90</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a2'</font>
 ;<br/>

<a NAME="E2:16_2_1_1"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">a2'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:16_2_1_1"/>
<font color="Maroon">o'</font>,<font color="Maroon">a2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_1"/>
<font color="Maroon">o'</font>,<font color="Maroon">a2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_1"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:16_2_1"/>
<font color="Maroon">b1'</font>,<font color="Maroon">a2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1'</font>,<font color="Maroon">a1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_1_2"/>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E2:16_2_1_2"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">a2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_1_2"/>
<font color="Maroon">b1'</font>,<font color="Maroon">a2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1'</font>,<font color="Maroon">a1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_2_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:16_2"/><i><font color="Green">E93</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">a2</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_2"/>
( <font color="Maroon">M</font> <a href="analmetr.html#NR6" target="_self">is_line</a>  &amp; <font color="Maroon">N</font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T62">ANALMETR:62</a></i>;<br/>
<a NAME="E2:16_2_2"/><b>then </b><i><font color="Green">E94</font></i>: 
( <font color="Maroon">M'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">N'</font> is <a href="aff_1.html#V1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E3:16_2_2"/><b>then </b>
( <font color="Maroon">M'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M'</font> &amp; <font color="Maroon">N'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">N'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:16_2_2"/><b>then </b>
( <font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font> &amp; <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a2'</font> &amp; <font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font> &amp; <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">b1'</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:16_2_2"/><b>then </b><i><font color="Green">E95</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">a2</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">b2</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2</font>,<font color="Maroon">b1</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_2"/><i><font color="Green">E96</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_2_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 ;<br/>

<a NAME="E2:16_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_2_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:16_2_2"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_2_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 ;<br/>

<a NAME="E2:16_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:16_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:16_2_2_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:16_2_2"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">a2</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T78">ANALMETR:78</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">d1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E5:16_2"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E6:16_2"/><i><font color="Green">E98</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font>,<font color="Maroon">d1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font> )
 <b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>reconsider </b><font color="Maroon">d1'</font> = <font color="Maroon">d1</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E9:16_2"/><i><font color="Green">E99</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E11:16_2"/><i><font color="Green">E100</font></i>: 
( <font color="Maroon">a1</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E12:16_2"/><i><font color="Green">E101</font></i>: 
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_3"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:16_2_3"/>
<font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">e2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_3"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">e2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_3"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_3"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_3"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:16_2_3"/><b>then </b><i><font color="Green">E113</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:16_2_3"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:16_2_3"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:16_2_3"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E18:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E20:16_2_3"/><b>then </b><i><font color="Green">E114</font></i>: 
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:16_2_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E22:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E23:16_2_3"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E24:16_2_3"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E25:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E26:16_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E27:16_2_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E14:16_2"/>
not <font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">e2'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">d2'</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E16:16_2"/><i><font color="Green">E115</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>,<font color="Maroon">d2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">e2'</font>,<font color="Maroon">d2'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">d2</font> = <font color="Maroon">d2'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E18:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E19:16_2"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E20:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E21:16_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E22:16_2"/><b>then </b><i><font color="Green">E118</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E23:16_2"/>
<font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_4"/>
<font color="Maroon">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:16_2_4"/><b>then </b><i><font color="Green">E119</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_4"/>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:16_2_4"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:16_2_4"/><b>then </b><i><font color="Green">E120</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:16_2_4"/>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:16_2_4"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:16_2_4"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:16_2_4"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E12:16_2_4"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:16_2_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E15:16_2_4"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:16_2_4"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E17:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_4"/><b>then </b><i><font color="Green">E122</font></i>: 
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E21:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E22:16_2_4"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:16_2_4"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E24:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:16_2_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E26:16_2_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E24:16_2"/><b>then </b><i><font color="Green">E123</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>,<font color="Maroon">d2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font> &amp; <font color="Maroon">a1</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E26:16_2"/><i><font color="Green">E124</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E28:16_2"/><i><font color="Green">E126</font></i>: 
( <font color="Maroon">b3</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d2</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E29:16_2"/><i><font color="Green">E127</font></i>: 
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_5"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">e2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:16_2_5"/>
<font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">e2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_5"/><b>then </b>
<font color="Maroon">d2'</font>,<font color="Maroon">e2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_5"/><b>then </b>
<font color="Maroon">d2</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_5"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_5"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_5"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_5"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_5"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:16_2_5"/><b>then </b><i><font color="Green">E129</font></i>: 
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_5"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:16_2_5"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_5"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E18:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:16_2_5"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E31:16_2"/>
not <font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">e2'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">d3'</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E33:16_2"/><i><font color="Green">E130</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>,<font color="Maroon">d3'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">e2'</font>,<font color="Maroon">d3'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">d3</font> = <font color="Maroon">d3'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E35:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">e2</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E36:16_2"/><b>then </b><i><font color="Green">E131</font></i>: 
<font color="Maroon">d2</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E37:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E38:16_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E39:16_2"/><b>then </b><i><font color="Green">E132</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E40:16_2"/>
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_6"/>
<font color="Maroon">d3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:16_2_6"/><b>then </b><i><font color="Green">E133</font></i>: 
<font color="Maroon">d2</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_6"/>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:16_2_6"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:16_2_6"/><b>then </b>
<font color="Maroon">d2</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:16_2_6"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:16_2_6"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_6"/><b>then </b><i><font color="Green">E134</font></i>: 
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_6"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_6"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_6"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#D1" target="_self">Def1</a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E13:16_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:16_2_6"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:16_2"/><b>then </b><i><font color="Green">E135</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font>,<font color="Maroon">d3</font> &amp; <font color="Maroon">b3</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E43:16_2"/><i><font color="Green">E136</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E45:16_2"/><i><font color="Green">E137</font></i>: 
( <font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d3</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/><a NAME="E46:16_2"/><i><font color="Green">E138</font></i>: 
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d3</font>,<font color="Maroon">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_7"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d3</font>,<font color="Maroon">e2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:16_2_7"/>
<font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d3'</font>,<font color="Maroon">e2'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_7"/><b>then </b>
<font color="Maroon">d3'</font>,<font color="Maroon">e2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_7"/><b>then </b>
<font color="Maroon">d3</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_7"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#D3" target="_self">Def3</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:16_2_7"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#D1" target="_self">Def1</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:16_2_7"/><b>then </b><i><font color="Green">E140</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:16_2_7"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_7"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:16_2_7"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:16_2_7"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#D7" target="_self">Def7</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E14:16_2_7"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:16_2_7"/><b>then </b><i><font color="Green">E141</font></i>: 
<font color="Maroon">b2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E16:16_2_7"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_7"/><b>then </b>
<font color="Maroon">b2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_7"/><b>then </b>
<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#D8" target="_self">Def8</a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E20:16_2_7"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E21:16_2_7"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">e1'</font> = <font color="Maroon">e1</font>, <font color="Maroon">e2'</font> = <font color="Maroon">e2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E48:16_2"/>
not <font color="Maroon">o'</font>,<font color="Maroon">e1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d3'</font>,<font color="Maroon">e2'</font>
 <b>by </b><i><a class="ref" href="conmetr.html#D4" target="_self">Def4</a>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon">d4'</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E50:16_2"/><i><font color="Green">E142</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">e1'</font>,<font color="Maroon">d4'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d3'</font>,<font color="Maroon">e2'</font>,<font color="Maroon">d4'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon">d4</font> = <font color="Maroon">d4'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E52:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d3</font>,<font color="Maroon">e2</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="conmetr.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E53:16_2"/><b>then </b><i><font color="Green">E143</font></i>: 
<font color="Maroon">d3</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d3</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E54:16_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="conmetr.html#D5" target="_self">Def5</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E55:16_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E56:16_2"/><b>then </b><i><font color="Green">E144</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="conmetr.html#D1" target="_self">Def1</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><b>take </b><font color="Maroon">d4</font> = <font color="Maroon">d4</font>;<br/><a NAME="E57:16_2"/>
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_8"/>
<font color="Maroon">d4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:16_2_8"/><b>then </b><i><font color="Green">E145</font></i>: 
<font color="Maroon">d3</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr.html#D7" target="_self">Def7</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:16_2_8"/>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:16_2_8"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E5:16_2_8"/><b>then </b>
<font color="Maroon">d3</font>,<font color="Maroon">o</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E6:16_2_8"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E7:16_2_8"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_8"/><b>then </b><i><font color="Green">E146</font></i>: 
<font color="Maroon">a3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_8"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_8"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_8"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E13:16_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:16_2_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:16_2_8"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E58:16_2"/><b>then </b><i><font color="Green">E147</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>,<font color="Maroon">d4</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d3</font>,<font color="Maroon">d4</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d4</font> )
 <b>by </b><i><a class="ref" href="conmetr.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr.html#D7" target="_self">Def7</a>, <a class="ref" href="conmetr.html#D8" target="_self">Def8</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E59:16_2"/><i><font color="Green">E148</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9"/><i><font color="Green">E149</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:16_2_9"/><i><font color="Green">E150</font></i>: 
( <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_9_1"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_1"/>
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:16_2_9_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:16_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:16_2_9_1_1"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_9_1_1"/><b>then </b><i><font color="Green">E155</font></i>: 
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_9_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_9_1_1"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9_1_1"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_9_1_1"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_9_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:16_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:16_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:16_2_9_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:16_2_9_1"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_2"/>
<font color="Maroon">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_9_1_2"/><b>then </b><i><font color="Green">E157</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_9_1_2"/>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E9:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:16_2_9_1_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_9_1_2"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9_1_2"/><b>then </b><i><font color="Green">E159</font></i>: 
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_9_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_9_1_2"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_9_1_2"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:16_2_9_1_2"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:16_2_9_1_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E23:16_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E24:16_2_9_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_9_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_9_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_9_1_3"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/>

<a NAME="E2:16_2_9_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_9_1_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16_2_9_1"/>
( <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E50</font></i></a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E5:16_2_9"/><b>then </b>
<font color="Maroon">d2'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:16_2_9"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:16_2_9"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_9"/><b>then </b>
<font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:16_2_9"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E10:16_2_9"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:16_2_9"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E12:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_9"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_9"/><b>then </b><i><font color="Green">E161</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E18:16_2_9"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:16_2_9"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:16_2_9"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:16_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E23:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E24:16_2_9"/><b>then </b><i><font color="Green">E162</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:16_2_9"/>
( <font color="Maroon">o</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E26:16_2_9"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E27:16_2_9"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E28:16_2_9"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E29:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E30:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E31:16_2_9"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E32:16_2_9"/><b>then </b><i><font color="Green">E163</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:16_2_9"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E34:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E35:16_2_9"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E36:16_2_9"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E37:16_2_9"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E38:16_2_9"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E39:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E40:16_2_9"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E41:16_2_9"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E60:16_2"/><i><font color="Green">E165</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b2</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_10"/><i><font color="Green">E166</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:16_2_10"/><i><font color="Green">E168</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:16_2_10"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E4:16_2_10"/><b>then </b><i><font color="Green">E169</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E5:16_2_10"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:16_2_10"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:16_2_10"/><b>then </b><i><font color="Green">E170</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E8:16_2_10"/><i><font color="Green">E171</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:16_2_10"/><i><font color="Green">E172</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_10"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E11:16_2_10"/><b>then </b><i><font color="Green">E173</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E12:16_2_10"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_10"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E14:16_2_10"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b2</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a3</font> )
 <b>by </b><i>, , , <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E61:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d1'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E62:16_2"/><b>then </b><i><font color="Green">E174</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E63:16_2"/><b>then </b><i><font color="Green">E175</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E64:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E65:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E66:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i>, <a class="txt" href="conmetr.html#E2:16"><i><font color="Green">E49</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E67:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E68:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E69:16_2"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E70:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E71:16_2"/><b>then </b><i><font color="Green">E176</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E72:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d2'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E73:16_2"/><b>then </b><i><font color="Green">E177</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E74:16_2"/><b>then </b><i><font color="Green">E178</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E75:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E76:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E77:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E78:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E79:16_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">o'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E80:16_2"/><b>then </b>
<font color="Maroon">d2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E81:16_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E82:16_2"/><b>then </b><i><font color="Green">E179</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E83:16_2"/>
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 <b>by </b><i>, <a class="txt" href="conmetr.html#E3:16"><i><font color="Green">E50</font></i></a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E84:16_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E85:16_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E86:16_2"/><b>then </b><i><font color="Green">E180</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 <b>by </b><i>, <a class="ref" href="conmetr.html#T2" target="_self">Th2</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/><a NAME="E87:16_2"/><i><font color="Green">E181</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E88:16_2"/><i><font color="Green">E182</font></i>: 
<font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E89:16_2"/><i><font color="Green">E183</font></i>: 
<font color="Maroon">d3</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E90:16_2"/><i><font color="Green">E184</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>,<font color="Maroon">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11"/><i><font color="Green">E185</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>,<font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:16_2_11"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:16_2_11_1"/><i><font color="Green">E188</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1_1"/>
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:16_2_11_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:16_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:16_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:16_2_11_1_1"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_11_1_1"/><b>then </b><i><font color="Green">E189</font></i>: 
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_11_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_11_1_1"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11_1_1"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_11_1_1"/><b>then </b>
<font color="Maroon">b3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_11_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:16_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:16_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E20:16_2_11_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_11_1"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_1_2"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/>

<a NAME="E2:16_2_11_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_11_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:16_2_11_1"/>
<font color="Maroon">a3</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:16_2_11_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:16_2_11_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:16_2_11_1"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E8:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:16_2_11_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:16_2_11_1"/><b>then </b><i><font color="Green">E191</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:16_2_11_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E14:16_2_11_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:16_2_11_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a>, <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:16_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E20:16_2_11_1"/><b>then </b><i><font color="Green">E192</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:16_2_11_1"/>
( <font color="Maroon">o</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:16_2_11_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E23:16_2_11_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E24:16_2_11_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T7" target="_self">Th7</a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E25:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E26:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E27:16_2_11_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E28:16_2_11_1"/><b>then </b><i><font color="Green">E194</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E29:16_2_11_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E30:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E31:16_2_11_1"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E32:16_2_11_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:16_2_11_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E34:16_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E35:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E36:16_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E37:16_2_11_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_11"/><i><font color="Green">E195</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_11"/><i><font color="Green">E196</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_11"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E8:16_2_11"/><b>then </b><i><font color="Green">E197</font></i>: 
<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:16_2_11"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_11"/><b>then </b><i><font color="Green">E198</font></i>: 
<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:16_2_11"/>
<font color="Maroon">b2'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_11_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_11_2"/>
<font color="Maroon">b2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3'</font>
 ;<br/>

<a NAME="E2:16_2_11_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_11_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:16_2_11"/><b>then </b>
<font color="Maroon">b2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T6" target="_self">Th6</a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E14:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">o'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:16_2_11"/><b>then </b><i><font color="Green">E199</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">d4'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_11"/>
( <font color="Maroon">o</font>,<font color="Maroon">a3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d4</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d4</font> )
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:16_2_11"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E19:16_2_11"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d4'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E20:16_2_11"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="conmetr.html#T7" target="_self">Th7</a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E21:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E22:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E23:16_2_11"/><b>then </b><i><font color="Green">E200</font></i>: 
<font color="Maroon">b2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E24:16_2_11"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E26:16_2_11"/><b>then </b>
<font color="Maroon">b2'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E27:16_2_11"/><b>then </b>
<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E28:16_2_11"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E29:16_2_11"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E91:16_2"/><i><font color="Green">E201</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_12"/>
<font color="Maroon">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d4</font>
 ;<br/>

<a NAME="E2:16_2_12"/><b>then </b><i><font color="Green">E202</font></i>: 
<font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:16_2_12"/>
<font color="Maroon">d2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_12_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_12_1"/>
<font color="Maroon">d2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:16_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_12_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:16_2_12"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:16_2_12"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:16_2_12"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:16_2_12"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:16_2_12"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:16_2_12"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E92:16_2"/><i><font color="Green">E203</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b3'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a3'</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E48</font></i></a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">A'</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E94:16_2"/><i><font color="Green">E204</font></i>: 
( <font color="Maroon">A'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">d1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">d3'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">b3'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E96:16_2"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">d1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_13"/>
<font color="Maroon">d1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3'</font>
 ;<br/>

<a NAME="E2:16_2_13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_13"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">K'</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E98:16_2"/><i><font color="Green">E206</font></i>: 
( <font color="Maroon">K'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">d2'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> &amp; <font color="Maroon">d4'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> &amp; <font color="Maroon">a1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon">K</font> = <font color="Maroon">K'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E100:16_2"/><i><font color="Green">E207</font></i>: 
not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_14"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:16_2_14"/>
<font color="Maroon">A'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_14"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="conmetr.html#T7" target="_self">Th7</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_14"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_14"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E101:16_2"/><i><font color="Green">E209</font></i>: 
not <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_15"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:16_2_15"/>
<font color="Maroon">A'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_15"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">d4'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_15"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_15"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E102:16_2"/>
<font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_16"/>
<font color="Maroon">A'</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E2:16_2_16"/><b>then </b><i><font color="Green">E211</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:16_2_16"/>
<font color="Maroon">K'</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, , <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E4:16_2_16"/><b>then </b>
<font color="Maroon">K</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_16"/>
<font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font>
 <b>by </b><i>, <a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a>, , <a class="ref" href="analmetr.html#T63">ANALMETR:63</a></i>;<br/>


</div><b>end;</b></div><a NAME="E103:16_2"/><b>then </b>
( <font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, , <a class="ref" href="conmetr.html#T4" target="_self">Th4</a>, <a class="ref" href="conmetr.html#T5" target="_self">Th5</a>, , <a class="ref" href="conmetr.html#T6" target="_self">Th6</a>, <a class="ref" href="conmetr.html#T7" target="_self">Th7</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E104:16_2"/><b>then </b><i><font color="Green">E212</font></i>: 
<font color="Maroon">d1</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, , , , </i>;<br/><a NAME="E105:16_2"/><i><font color="Green">E213</font></i>: 
( <font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">d3</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">a2</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_17"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E2:16_2_17"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_17_1"/>
<font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3</font>
 ;<br/>

<a NAME="E2:16_2_17_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_17_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:16_2_17"/><i><font color="Green">E216</font></i>: 
( <font color="Maroon">d3</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font> or <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> )
 
<b>by </b><i>, <a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:16_2_17"/>
<font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_17_2"/>
<font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 ;<br/>

<a NAME="E2:16_2_17_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_17_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:16_2_17"/>
( <font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">d3</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">a2</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a1</font> )
 <b>by </b><i>, , , , <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E71</font></i></a>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div><a NAME="E106:16_2"/><i><font color="Green">E217</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:16_2_18"/><b>then </b><i><font color="Green">E218</font></i>: 
<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:16_2_18"/><b>then </b><i><font color="Green">E219</font></i>: 
<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:16_2_18"/>
<font color="Maroon">b3'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_18_1"/>
<font color="Maroon">b3'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2'</font>
 ;<br/>

<a NAME="E2:16_2_18_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_18_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:16_2_18"/><b>then </b>
<font color="Maroon">b3'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E71</font></i></a>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E9:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:16_2_18"/><b>then </b><i><font color="Green">E220</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:16_2_18"/><i><font color="Green">E221</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:16_2_18"/><b>then </b><i><font color="Green">E222</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E72</font></i></a>, <a class="txt" href="conmetr.html#E9:16"><i><font color="Green">E73</font></i></a>, <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon">o'</font> = <font color="Maroon">o</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">a2'</font> = <font color="Maroon">a2</font>, <font color="Maroon">a3'</font> = <font color="Maroon">a3</font>, <font color="Maroon">d2'</font> = <font color="Maroon">d2</font>, <font color="Maroon">d4'</font> = <font color="Maroon">d4</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E15:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:16_2_18"/><b>then </b><i><font color="Green">E223</font></i>: 
<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_18"/><b>then </b><i><font color="Green">E224</font></i>: 
<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_18"/>
<font color="Maroon">a3'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_18_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_18_2"/>
<font color="Maroon">a1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3'</font>
 ;<br/>

<a NAME="E2:16_2_18_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_18_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:16_2_18"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">a2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E22:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:16_2_18"/><b>then </b><i><font color="Green">E225</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E24:16_2_18"/><i><font color="Green">E226</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:16_2_18"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E26:16_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a2'</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E27:16_2_18"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b3</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">b1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a1</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>,<font color="Maroon">a2</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E1:16"><i><font color="Green">E48</font></i></a>, , <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">d1'</font> = <font color="Maroon">d1</font>, <font color="Maroon">d2'</font> = <font color="Maroon">d2</font>, <font color="Maroon">d3'</font> = <font color="Maroon">d3</font>, <font color="Maroon">d4'</font> = <font color="Maroon">d4</font>, <font color="Maroon">b3'</font> = <font color="Maroon">b3</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">a2'</font> = <font color="Maroon">a2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/><a NAME="E108:16_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">A'</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E110:16_2"/><i><font color="Green">E227</font></i>: 
( <font color="Maroon">A'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">d1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">d3'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">b3'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E112:16_2"/><i><font color="Green">E228</font></i>: 
<font color="Maroon">d1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_19"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_19"/>
<font color="Maroon">d1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3'</font>
 ;<br/>

<a NAME="E2:16_2_19"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:16_2_19"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E113:16_2"/><i><font color="Green">E229</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>,<font color="Maroon">b1'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E114:16_2"/><i><font color="Green">E230</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a2'</font> )
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon">K'</font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E116:16_2"/><i><font color="Green">E231</font></i>: 
( <font color="Maroon">K'</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">d2'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> &amp; <font color="Maroon">d4'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> &amp; <font color="Maroon">a1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon">K</font> = <font color="Maroon">K'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/><a NAME="E118:16_2"/><i><font color="Green">E232</font></i>: 
not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_20"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_20"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:16_2_20"/>
<font color="Maroon">A'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_20"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">d2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_20"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_20"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E119:16_2"/><i><font color="Green">E234</font></i>: 
not <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_21"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_21"/><i><font color="Green">E235</font></i>: 
<font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:16_2_21"/>
<font color="Maroon">A'</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:16_2_21"/><b>then </b>
<font color="Maroon">d1'</font>,<font color="Maroon">d4'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:16_2_21"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">d4</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_21"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div><a NAME="E120:16_2"/>
<font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_22"><b>proof </b></a><div class="add">

<a NAME="E1:16_2_22"/>
<font color="Maroon">A'</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">d1'</font>,<font color="Maroon">d3'</font>
 
<b>by </b><i>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E71</font></i></a>, <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E2:16_2_22"/><b>then </b><i><font color="Green">E236</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:16_2_22"/>
<font color="Maroon">K'</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">d2'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, , <a class="ref" href="aff_1.html#T38">AFF_1:38</a></i>;<br/>
<a NAME="E4:16_2_22"/><b>then </b>
<font color="Maroon">K</font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4">Line</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:16_2_22"/>
<font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font>
 <b>by </b><i>, <a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E71</font></i></a>, , <a class="ref" href="analmetr.html#T63">ANALMETR:63</a></i>;<br/>


</div><b>end;</b></div><a NAME="E121:16_2"/><b>then </b>
( <font color="Maroon">A</font> <a href="analmetr.html#R10">_|_</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="conmetr.html#T3" target="_self">Th3</a>, , <a class="txt" href="conmetr.html#E7:16"><i><font color="Green">E71</font></i></a>, <a class="txt" href="conmetr.html#E8:16"><i><font color="Green">E72</font></i></a>, <a class="txt" href="conmetr.html#E9:16"><i><font color="Green">E73</font></i></a>, , , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E122:16_2"/><b>then </b>
<font color="Maroon">d1</font>,<font color="Maroon">d4</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">a2</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E123:16_2"/><b>then </b><i><font color="Green">E237</font></i>: 
( <font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3</font>,<font color="Maroon">a2</font> or <font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d4</font> )
 <b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/><a NAME="E124:16_2"/>
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_23"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_2_23"/><i><font color="Green">E238</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d4</font>
 ;<br/>

<a NAME="E2:16_2_23"/><i><font color="Green">E239</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E3:16_2_23"/><i><font color="Green">E240</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">d1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<a NAME="E7:16_2_23"/><b>then </b><i><font color="Green">E241</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">d4'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:16_2_23"/><b>then </b><i><font color="Green">E242</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:16_2_23"/><i><font color="Green">E243</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">d4'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E12:16_2_23"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">d4'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T19">AFF_1:19</a></i>;<br/>
<a NAME="E13:16_2_23"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="conmetr.html#T1" target="_self">Th1</a>, , , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E14:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:16_2_23"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:16_2_23"/><b>then </b><i><font color="Green">E244</font></i>: 
<font color="Maroon">a3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E18:16_2_23"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">o'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:16_2_23"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:16_2_23"/><b>then </b>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E21:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E22:16_2_23"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E23:16_2_23"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div><a NAME="E125:16_2"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b3'</font>,<font color="Maroon">a2'</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E126:16_2"/><b>then </b>
<font color="Maroon">a1'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2'</font>,<font color="Maroon">b3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E127:16_2"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:16"/>
<font color="Maroon">a1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 <b>by </b><i/>;<br/>


</div>
