<?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="E1:5"/><i><font color="Green">E26</font></i>: 
 <a href="conaffm.html#NR5" target="_self">LIN_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="conaffm.html#D6" target="_self">CONAFFM:def 6</a><br/><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">a1</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">b1</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>let </b><font color="Maroon">c1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/>













<b>assume </b><a NAME="E2:5"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</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">b</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">c</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font> &amp; not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">b1</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</font>, <font color="Maroon">c1'</font> = <font color="Maroon">c1</font>, <font color="Maroon">o'</font> = <font color="Maroon">o</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><a NAME="E1:5_1"/>
 ex <font color="Olive">b2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Olive">b2</font> &amp; <font color="Maroon">c1</font>,<font color="Olive">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:5_1_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:5_1_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">c1</font>,<font color="Maroon">x</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<a NAME="E5:5_1_1"/><i><font color="Green">E30</font></i>: 
not <font color="Maroon">o</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">x</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">y'</font> = <font color="Maroon">y</font>, <font color="Maroon">x'</font> = <font color="Maroon">x</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="E3:5_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">y'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1'</font>,<font color="Maroon">x'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:5_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">y'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:5_1_1_1"/><b>then </b>
( <font color="Maroon">o'</font>,<font color="Maroon">y'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E6:5_1_1_1"/><b>then </b>
<font color="Maroon">c1'</font>,<font color="Maroon">x'</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="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E7:5_1_1_1"/><b>then </b>
<font color="Maroon">c1</font>,<font color="Maroon">x</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="E8:5_1_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:5_1_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E10:5_1_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:5_1_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T82">ANALMETR:82</a></i>;<br/>
<a NAME="E12:5_1_1_1"/><b>then </b>
<font color="Maroon">b'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E13:5_1_1_1"/><b>then </b>
<font color="Maroon">b'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</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="E14:5_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</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="E15:5_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E16:5_1_1_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E17:5_1_1_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:5_1_1_1"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E19:5_1_1_1"/><b>then </b>
( <font color="Maroon">o'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:5_1_1_1"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E21:5_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c'</font>,<font color="Maroon">a'</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="E22:5_1_1_1"/>
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">y'</font> = <font color="Maroon">y</font>, <font color="Maroon">x'</font> = <font color="Maroon">x</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="E7:5_1_1"/>
not <font color="Maroon">o'</font>,<font color="Maroon">y'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1'</font>,<font color="Maroon">x'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">b2'</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="E9:5_1_1"/><i><font color="Green">E45</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">y'</font>,<font color="Maroon">b2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c1'</font>,<font color="Maroon">x'</font>,<font color="Maroon">b2'</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">b2</font> = <font color="Maroon">b2'</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="E11:5_1_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">c1</font>,<font color="Maroon">x</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:5_1_1"/><b>then </b>
<font color="Maroon">c1</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</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="E13:5_1_1"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c1</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E14:5_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">y'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:5_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">o'</font>,<font color="Maroon">y'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E16:5_1_1"/>
<font color="Maroon">o'</font>,<font color="Maroon">y'</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="E17:5_1_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="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E18:5_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">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:5_1_1"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="analmetr.html#R5">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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E20:5_1_1"/>
<font color="Maroon">c1</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="5_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_1_2"/>
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 ;<br/>

<a NAME="E2:5_1_1_2"/><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">c1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:5_1_1_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:5_1_1_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<b>hence </b><a NAME="E5:5_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E21:5_1_1"/>
 ex <font color="Olive">b2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Olive">b2</font> &amp; <font color="Maroon">c1</font>,<font color="Olive">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b2</font> )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">b2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:5_1"/><i><font color="Green">E49</font></i>: 
(  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Maroon">b2</font> &amp; <font color="Maroon">c1</font>,<font color="Maroon">b2</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> )
 ;<br/><b>reconsider </b><font color="Maroon">b2'</font> = <font color="Maroon">b2</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="E5:5_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font> &amp; <font color="Maroon">o</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="5_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:5_1_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_1_2_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">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:5_1_2_1"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:5_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E4:5_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, , <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:5_1_2"/>
<font color="Maroon">o</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="5_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_2_2"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 ;<br/>

<a NAME="E2:5_1_2_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:5_1_2_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:5_1_2_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:5_1_2_2"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">o'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E6:5_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">o'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:5_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:5_1_2_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">o'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:5_1_2_2"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:5_1_2_2"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E11:5_1_2_2"/><b>then </b>
( <font color="Maroon">o'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:5_1_2_2"/><b>then </b>
<font color="Maroon">o'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i>, <a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E13:5_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">c'</font>,<font color="Maroon">a'</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="E14:5_1_2_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="E3:5_1_2"/>
( <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">b2</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div><a NAME="E6:5_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b2</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/><a NAME="E7:5_1"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">b2</font>
 <b>by </b><i>, , , , </i>;<br/><a NAME="E8:5_1"/>
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:5_1_3"/>
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1_3_1"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">a1</font>
 ;<br/>

<a NAME="E2:5_1_3_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</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="E3:5_1_3_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:5_1_3_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:5_1_3"/><b>then </b><i><font color="Green">E55</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>,<font color="Maroon">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:5_1_3"/><i><font color="Green">E56</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:5_1_3"/><i><font color="Green">E57</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:5_1_3"/><i><font color="Green">E58</font></i>: 
 <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="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:5_1_3"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">a'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">b1'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:5_1_3"/>
<font color="Maroon">a'</font>,<font color="Maroon">a1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">b2'</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E8:5_1_3"/>
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 <b>by </b><i>, , , , , <a class="ref" href="aff_1.html#T70">AFF_1:70</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E9:5_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:5"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 ;<br/>


</div>
