<?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="E1:17"/><i><font color="Green">E48</font></i>: 
 <a href="conaffm.html#NR3" target="_self">3H_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="E2:17"/><i><font color="Green">E49</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="E5:17"/>
( <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="E6:17"/><b>then </b><i><font color="Green">E50</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="E7:17"/><b>then </b><i><font color="Green">E71</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/>
<a NAME="E8:17"/><i><font color="Green">E72</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>  st  <a href="analmetr.html#R5">LIN</a> <font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font> holds <br/>(  <a href="analmetr.html#R5">LIN</a> <font color="Olive">a</font>,<font color="Olive">c</font>,<font color="Olive">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b</font>,<font color="Olive">a</font>,<font color="Olive">c</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">a</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">c</font>,<font color="Olive">a</font>,<font color="Olive">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Olive">c</font>,<font color="Olive">b</font>,<font color="Olive">a</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E73</font></i>: 
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</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="E3:17_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:17_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">c'</font>,<font color="Maroon">b'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">a'</font>,<font color="Maroon">c'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">a'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:17_1"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E74</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/><a NAME="E2:17_2"/><i><font color="Green">E76</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font>
 ;<br/>

<a NAME="E2:17_2_1"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">b1'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:17_2_1"/>
<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="E4:17_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">b2'</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="E5:17_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="E3:17_2"/><i><font color="Green">E78</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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_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">b3'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_2_2"/>
 <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/>


</div><b>end;</b></div><a NAME="E4:17_2"/>
<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_3"/>
<font color="Maroon">a1</font>,<font color="Maroon">b1</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#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E2:17_2_3"/>
<font color="Maroon">a1'</font>,<font color="Maroon">b1'</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/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:17_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="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E79</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_3"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3</font>
 ;<br/><a NAME="E2:17_3"/><i><font color="Green">E81</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">a1'</font>
 ;<br/>

<a NAME="E2:17_3_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">a1'</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="E3:17_3_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="E4:17_3_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="E5:17_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="E3:17_3"/><i><font color="Green">E83</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_3_2"/>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</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/>


</div><b>end;</b></div><a NAME="E4:17_3"/>
<font color="Maroon">b1'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1'</font>,<font color="Maroon">a2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_3_3"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">a1</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="E2:17_3_3"/>
<font color="Maroon">b1</font>,<font color="Maroon">a2</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="E3:17_3_3"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a2</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:17_3_3"/>
<font color="Maroon">b1'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1'</font>,<font color="Maroon">a2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:17_3"/><b>then </b>
<font color="Maroon">a1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E6:17_3"/><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="E7:17_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="analmetr.html#T48">ANALMETR:48</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> )
 ;<br/><a NAME="E2:17_4"/><i><font color="Green">E86</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="17_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_1"/><i><font color="Green">E87</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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_1_1"/>
( <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="E2:17_4_1_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a3'</font>,<font color="Maroon">a1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a3'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">b3'</font> &amp;  <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_1_1"/>
(  <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_4_1"/>
( 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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_1_2"/>
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font> or  <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="E2:17_4_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> or  <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="E3:17_4_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> or  <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="E4:17_4_1_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="E3:17_4_1"/>
(  <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></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green">E88</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_2"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/><a NAME="E2:17_4_2"/><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">a2</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/><a NAME="E3:17_4_2"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2'</font>,<font color="Maroon">a2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/><a NAME="E4:17_4_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">o</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:17_4_2"/><b>then </b><i><font color="Green">E91</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:17_4_2"/><i><font color="Green">E92</font></i>: 
<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="17_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_2_1"/>
<font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/>

<a NAME="E2:17_4_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="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_2_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="E7:17_4_2"/>
<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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:17_4_2"/><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">a2</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/><a NAME="E9:17_4_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">o</font>,<font color="Maroon">a2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/><a NAME="E10:17_4_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a3</font>,<font color="Maroon">a2</font>
 <b>by </b><i/>;<br/><a NAME="E11:17_4_2"/><b>then </b><i><font color="Green">E93</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="analmetr.html#T55">ANALMETR:55</a></i>;<br/><a NAME="E12:17_4_2"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">a3'</font>
 ;<br/>

<a NAME="E2:17_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5">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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:17_4_2_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">o</font>,<font color="Maroon">a3</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:17_4_2_2"/><b>then </b><i><font color="Green">E94</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_2_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">o</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:17_4_2_2"/><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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_2_2"/><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="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E8:17_4_2_2"/>
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="E13:17_4_2"/><b>then </b>
<font color="Maroon">a3'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2'</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E14:17_4_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="17_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font>
 ;<br/><a NAME="E2:17_4_3"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a2</font>,<font color="Maroon">a3</font>,<font color="Maroon">b3</font>
 ;<br/>

<a NAME="E2:17_4_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a2</font>,<font color="Maroon">b3</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:17_4_3_1"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">a3</font>,<font color="Maroon">a2</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#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:17_4_3_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">a3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1_1"/>
<font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font>
 ;<br/>

<a NAME="E2:17_4_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font>,<font color="Maroon">b1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:17_4_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b1</font>,<font color="Maroon">a3</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:17_4_3_1_1"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">b2</font>,<font color="Maroon">b1</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_3_1_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:17_4_3_1_1"/><b>then </b>
<font color="Maroon">b2</font>,<font color="Maroon">b1</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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_3_1_1"/><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="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E8:17_4_3_1_1"/>
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="E5:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a2</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:17_4_3_1"/><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">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:17_4_3_1"/><b>then </b><i><font color="Green">E99</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">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:17_4_3_1"/><i><font color="Green">E100</font></i>: 
<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="17_4_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_1_2"/>
<font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/>

<a NAME="E2:17_4_3_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="E3:17_4_3_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="E9:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:17_4_3_1"/><b>then </b>
<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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:17_4_3_1"/><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">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:17_4_3_1"/><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">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E13:17_4_3_1"/><b>then </b><i><font color="Green">E101</font></i>: 
<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="E14:17_4_3_1"/><i><font color="Green">E112</font></i>: 
not  <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="E15:17_4_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E16:17_4_3_1"/><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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E17:17_4_3_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><b>then consider </b><font color="Maroon">c1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:17_4_3"/><i><font color="Green">E113</font></i>: 
( <font color="Maroon">c1</font>,<font color="Maroon">a2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">c1</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a2</font>,<font color="Maroon">b3</font> &amp; <font color="Maroon">c1</font>,<font color="Maroon">b3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a2</font>,<font color="Maroon">a3</font> )
 <b>by </b><i>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">c1'</font> = <font color="Maroon">c1</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/><div><i><font color="Green">E114</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/><a NAME="E2:17_4_3_2"/><i><font color="Green">E116</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="E3:17_4_3_2"/><i><font color="Green">E118</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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_2_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/>
<b>hence </b><a NAME="E2:17_4_3_2_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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:17_4_3_2"/>
<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="17_4_3_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_2_2"/>
<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="17_4_3_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_2_2_1"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_2_2_1"/>
<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="E3:17_4_3_2_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">b2'</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="E4:17_4_3_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="E2:17_4_3_2_2"/><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="E3:17_4_3_2_2"/>
<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="E5:17_4_3_2"/><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="E6:17_4_3_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#T11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E7:17_4_3_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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_4_3_3"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font>
 ;<br/><a NAME="E2:17_4_3_3"/><i><font color="Green">E121</font></i>: 
<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="17_4_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_1"/><i><font color="Green">E122</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:17_4_3_3_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">a2</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#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:17_4_3_3_1"/><b>then </b>
<font color="Maroon">a2</font>,<font color="Maroon">a1</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="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_1"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">a1</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#T82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E6:17_4_3_3_1"/>
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="E3:17_4_3_3"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a2</font>,<font color="Maroon">a1</font>,<font color="Maroon">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_2"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a2</font>,<font color="Maroon">a1</font>,<font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>,<font color="Maroon">a2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:17_4_3_3_2"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:17_4_3_3_2"/><b>then </b><i><font color="Green">E123</font></i>: 
<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#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_2"/><i><font color="Green">E124</font></i>: 
<font color="Maroon">a2</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="17_4_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_2_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_2_1"/>
<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="E3:17_4_3_3_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">b2'</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="E4:17_4_3_3_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="E6:17_4_3_3_2"/>
<font color="Maroon">a2</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#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:17_4_3_3_2"/><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">b2</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:17_4_3_3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a3</font>,<font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E9:17_4_3_3_2"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E5:17_4_3_3"/><i><font color="Green">E127</font></i>: 
( <font color="Maroon">c2</font>,<font color="Maroon">a2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">c2</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a2</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">c2</font>,<font color="Maroon">b1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a2</font>,<font color="Maroon">a1</font> )
 <b>by </b><i>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">c2'</font> = <font color="Maroon">c2</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="E7:17_4_3_3"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3"/><i><font color="Green">E129</font></i>: 
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">c2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">a2</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E2:17_4_3_3_3_1"/>
<font color="Maroon">a2</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="17_4_3_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_1_1"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_1_1"/><i><font color="Green">E132</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="17_4_3_3_3_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_1_1_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="E2:17_4_3_3_3_1_1_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="E3:17_4_3_3_3_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="E3:17_4_3_3_3_1_1"/><i><font color="Green">E133</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1_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/>
<b>hence </b><a NAME="E2:17_4_3_3_3_1_1_2"/>
 <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/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_3_1_1"/>
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_1_1_3"/>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_3_1_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">b2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_4_3_3_3_1_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="E3:17_4_3_3_3_1"/><b>then </b>
<font color="Maroon">b2</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_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">c1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:17_4_3_3_3_1"/><b>then </b><i><font color="Green">E134</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">c1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:17_4_3_3_3_1"/>
<font color="Maroon">a2</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b2</font>,<font color="Maroon">b1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E8:17_4_3_3_3_1"/><b>then </b>
<font color="Maroon">b2</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c2</font>,<font color="Maroon">b1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:17_4_3_3_3_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:17_4_3_3_3_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">c2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:17_4_3_3_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">c2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E12:17_4_3_3_3_1"/>
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp; <font color="Maroon">c2</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/>


</div><b>end;</b></div>
<a NAME="E2:17_4_3_3_3"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">c1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">c2'</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:17_4_3_3_3"/><b>then </b><i><font color="Green">E135</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c1'</font>,<font color="Maroon">c2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:17_4_3_3_3"/><i><font color="Green">E136</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">c1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">c1'</font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_2"/><b>then </b><i><font color="Green">E137</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c1'</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="E3:17_4_3_3_3_2"/>
<font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_2_1"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">o'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1'</font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E3:17_4_3_3_3_2_1"/><b>then </b>
<font color="Maroon">b3</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#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_2_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#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:17_4_3_3_3_2_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="E6:17_4_3_3_3_2_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/>
<b>hence </b><a NAME="E7:17_4_3_3_3_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="E4:17_4_3_3_3_2"/><b>then </b><i><font color="Green">E139</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="E5:17_4_3_3_3_2"/>
<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="E6:17_4_3_3_3_2"/><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="E7:17_4_3_3_3_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>
<a NAME="E5:17_4_3_3_3"/>
<font color="Maroon">a2'</font>,<font color="Maroon">c1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2'</font>,<font color="Maroon">c2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_3_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_3_3"/><i><font color="Green">E140</font></i>: 
<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="17_4_3_3_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_3_3_1"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_3_3_1"/>
<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="E3:17_4_3_3_3_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">b2'</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="E4:17_4_3_3_3_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="E2:17_4_3_3_3_3"/>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c1</font>,<font color="Maroon">a2</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:17_4_3_3_3_3"/><b>then </b>
<font color="Maroon">c2</font>,<font color="Maroon">a2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">a2</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_3_3"/><b>then </b>
<font color="Maroon">a2</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2</font>,<font color="Maroon">c2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E5:17_4_3_3_3_3"/>
<font color="Maroon">a2'</font>,<font color="Maroon">c1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a2'</font>,<font color="Maroon">c2'</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="E6:17_4_3_3_3"/>
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font>
 <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="E8:17_4_3_3"/>
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="17_4_3_3_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_4"/>
 <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="E2:17_4_3_3_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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:17_4_3_3_4"/>
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>then consider </b><font color="Maroon">c3</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E10:17_4_3_3"/><i><font color="Green">E142</font></i>: 
( <font color="Maroon">c3</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">b2</font> &amp; <font color="Maroon">c3</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">b2</font> &amp; <font color="Maroon">c3</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a3</font>,<font color="Maroon">a1</font> )
 <b>by </b><i>, <a class="ref" href="conaffm.html#D3">CONAFFM:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">c3'</font> = <font color="Maroon">c3</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="E12:17_4_3_3"/><i><font color="Green">E143</font></i>: 
<font color="Maroon">c2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5"/><i><font color="Green">E144</font></i>: 
( <font color="Maroon">c2'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N'</font> &amp; <font color="Maroon">c3'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N'</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_1"/>
<font color="Maroon">a2</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E2:17_4_3_3_5_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c2</font>,<font color="Maroon">b1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">c2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:17_4_3_3_5_1"/><b>then </b><i><font color="Green">E145</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">c2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:17_4_3_3_5_1"/>
<font color="Maroon">a3</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E7:17_4_3_3_5_1"/><b>then </b>
<font color="Maroon">c3</font>,<font color="Maroon">b2</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="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E8:17_4_3_3_5_1"/><b>then </b>
<font color="Maroon">b2</font>,<font color="Maroon">b3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b2</font>,<font color="Maroon">c3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E9:17_4_3_3_5_1"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>,<font color="Maroon">c3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E10:17_4_3_3_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">c3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E11:17_4_3_3_5_1"/>
( <font color="Maroon">c2'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N'</font> &amp; <font color="Maroon">c3'</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/>


</div><b>end;</b></div>
<a NAME="E2:17_4_3_3_5"/><i><font color="Green">E146</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c2'</font>,<font color="Maroon">c3'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_2"/>
<font color="Maroon">o'</font>,<font color="Maroon">c2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">c3'</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_5_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c2'</font>,<font color="Maroon">c3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_5"/><i><font color="Green">E147</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">c2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3"/><i><font color="Green">E148</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">c2'</font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3"/><i><font color="Green">E149</font></i>: 
<font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3_1"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">o'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2'</font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3_1"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">a2</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="17_4_3_3_5_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_3_1_1"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_3_1_1"/>
<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="E3:17_4_3_3_5_3_1_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">b2'</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="E4:17_4_3_3_5_3_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_4_3_3_5_3_1"/><i><font color="Green">E156</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b3</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_3_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a1</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="E5:17_4_3_3_5_3_1"/><b>then </b>
<font color="Maroon">b3</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#D3" target="_self">Def3</a>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:17_4_3_3_5_3_1"/><b>then </b>
<font color="Maroon">b2</font>,<font color="Maroon">b3</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="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E7:17_4_3_3_5_3_1"/><b>then </b>
 <a href="analmetr.html#R5">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="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:17_4_3_3_5_3_1"/><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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:17_4_3_3_5_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="E3:17_4_3_3_5_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c2'</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="E4:17_4_3_3_5_3"/><b>then </b><i><font color="Green">E157</font></i>: 
<font color="Maroon">a1'</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="E5:17_4_3_3_5_3"/>
<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="E6:17_4_3_3_5_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">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="E7:17_4_3_3_5_3"/>
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="E4:17_4_3_3_5"/>
<font color="Maroon">a1'</font>,<font color="Maroon">c2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">c3'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_5_4"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_5_4"/>
<font color="Maroon">a2</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="17_4_3_3_5_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_5_4_1"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:17_4_3_3_5_4_1"/>
<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="E3:17_4_3_3_5_4_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">b2'</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="E4:17_4_3_3_5_4_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="E2:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c2</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">c2</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c3</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:17_4_3_3_5_4"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">c2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E5:17_4_3_3_5_4"/>
<font color="Maroon">a1'</font>,<font color="Maroon">c2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1'</font>,<font color="Maroon">c3'</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="E5:17_4_3_3_5"/>
<font color="Maroon">c2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c3</font>
 <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="E13:17_4_3_3"/>
<font color="Maroon">c1</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="17_4_3_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6"/><i><font color="Green">E161</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/>

<a NAME="E2:17_4_3_3_6"/><i><font color="Green">E162</font></i>: 
<font color="Maroon">a2</font>,<font color="Maroon">a3</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b2</font>,<font color="Maroon">b3</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T78">ANALMETR:78</a></i>;<br/>
<a NAME="E3:17_4_3_3_6"/>
<font color="Maroon">a2</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="17_4_3_3_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6_1"/><i><font color="Green">E163</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 ;<br/>

<a NAME="E2:17_4_3_3_6_1"/><i><font color="Green">E165</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="17_4_3_3_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_4_3_3_6_1_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="E2:17_4_3_3_6_1_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="E3:17_4_3_3_6_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="E3:17_4_3_3_6_1"/><i><font color="Green">E166</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_6_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_6_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/>
<b>hence </b><a NAME="E2:17_4_3_3_6_1_2"/>
 <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/>


</div><b>end;</b></div>
<a NAME="E4:17_4_3_3_6_1"/>
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4_3_3_6_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:17_4_3_3_6_1_3"/>
<font color="Maroon">a3'</font>,<font color="Maroon">b2'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E2:17_4_3_3_6_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">b2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_4_3_3_6_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="E4:17_4_3_3_6"/><b>then </b>
<font color="Maroon">a3</font>,<font color="Maroon">b3</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="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:17_4_3_3_6"/><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#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:17_4_3_3_6"/><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="E7:17_4_3_3_6"/><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/>
<b>hence </b><a NAME="E8:17_4_3_3_6"/>
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="E14:17_4_3_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="analmetr.html#T85">ANALMETR:85</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:17_4_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/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:17_4"/>
<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><b>end;</b></div>
<b>hence </b><a NAME="E12:17"/>
<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>
