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

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

<a NAME="E1:20"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a>  implies <font color="Maroon">X</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM2">Subset</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">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<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">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>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">b1</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="E1:20_1_1"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <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">b</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">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">Y</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">Z</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">M</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font> )
 ;<br/><b>assume </b><a NAME="E2:20_1_1"/><i><font color="Green">E48</font></i>: 
not <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 ;<br/><div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM2">Subset</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">o</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<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">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>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">b1</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>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>;<br/><b>assume </b><a NAME="E1:20_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a> 
 ;<br/><b>assume </b><a NAME="E2:20_1_1_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <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">b</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">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">Y</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">Z</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">M</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">d</font> )
 ;<br/><a NAME="E3:20_1_1_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>,<font color="Maroon">d</font> or <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1"/><i><font color="Green">E54</font></i>: 
( not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>,<font color="Maroon">d</font> &amp; not <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font> )
 ;<br/>

<a NAME="E2:20_1_1_1_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c</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">a1</font> &amp; <font color="Maroon">b</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="20_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1"/><i><font color="Green">E56</font></i>: 
(  not <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> or  not <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> or  not <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> )
 ;<br/>

<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 ;<br/><a NAME="E2:20_1_1_1_1_1_1"/><i><font color="Green">E59</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">a</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="E3:20_1_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_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="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E61</font></i>: 
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E6:20_1_1_1_1_1_1"/>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E8:20_1_1_1_1_1_1"/><i><font color="Green">E63</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_1_2"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_1_1_1_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_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">b1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_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">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E12:20_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E13:20_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E65</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/><a NAME="E2:20_1_1_1_1_1_2"/><i><font color="Green">E68</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_2_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_2_1"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_2"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_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">b1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_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">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E6:20_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_2"/><i><font color="Green">E71</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_2_2"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_2_2"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:20_1_1_1_1_1_2"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E9:20_1_1_1_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">c1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E10:20_1_1_1_1_1_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">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E11:20_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E12:20_1_1_1_1_1_2"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_1_3"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/><a NAME="E2:20_1_1_1_1_1_3"/><i><font color="Green">E74</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_3_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_3_1"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_3_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_3_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_3_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_1_3"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E4:20_1_1_1_1_1_3"/><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="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_1_1_1_3"/><b>then </b><i><font color="Green">E76</font></i>: 
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E6:20_1_1_1_1_1_3"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E7:20_1_1_1_1_1_3"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E8:20_1_1_1_1_1_3"/><i><font color="Green">E78</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_1_3_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_1_3_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_1_3_2"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_1_3_2"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_1_3_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_1_3_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_1_1_1_3"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_1_1_3"/><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">c1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E12:20_1_1_1_1_1_3"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E13:20_1_1_1_1_1_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div><i><font color="Green">E81</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_1"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_1_1"/><i><font color="Green">E85</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_1_1_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_1_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_1_1_2"/>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</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/>
<a NAME="E5:20_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</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/>
<a NAME="E6:20_1_1_1_1_2_1_1_2"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</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="E3:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_1_2_1"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_1_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_1_1_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:20_1_1_1_1_2_1_1_2"/>
<font color="Maroon">a1</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b</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/>
<b>hence </b><a NAME="E10:20_1_1_1_1_2_1_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_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="E3:20_1_1_1_1_2_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_1_2"/><i><font color="Green">E93</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E3:20_1_1_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_1_2_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_1_2"/><i><font color="Green">E95</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_1_2_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c1</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#T65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_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">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E6:20_1_1_1_1_2_1_2_2"/><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">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_1_2_2"/><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">c1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">c1</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="E9:20_1_1_1_1_2_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_1_1_2_1_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_1_2"/>
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>hence </b><a NAME="E4:20_1_1_1_1_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1"/><i><font color="Green">E99</font></i>: 
(  not <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> or  not <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 ;<br/>

<div><i><font color="Green">E100</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E103</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_1_2"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_1_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1_2_2_1"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2"/><i><font color="Green">E104</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">a1</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="20_1_1_1_1_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2"/><i><font color="Green">E105</font></i>: 
(  not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> or  not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> )
 ;<br/>

<div><i><font color="Green">E106</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_2_1"/><b>then </b><i><font color="Green">E107</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_2_2"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_2_2"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">o</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="20_1_1_1_1_2_2_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2_1"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_2_2_1"/><i><font color="Green">E111</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_2_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_2_2_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b><i><font color="Green">E112</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_2_2_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_2_2_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_2_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_2_2_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_2_2_1"/><b>then </b><i><font color="Green">E113</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</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="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</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="E7:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</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="E8:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_2_2_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">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_2_2_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">b1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_2_2_1"/><b>then </b><i><font color="Green">E114</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_2_2_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_2_2_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E15:20_1_1_1_1_2_2_2_2_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2_2_2"/>
<font color="Maroon">o</font>,<font color="Maroon">a1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_2_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_1_1_2_2_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1_2_2_2"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_1_1_2_2"/><i><font color="Green">E115</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_1_1_2_2"/><i><font color="Green">E116</font></i>: 
( <font color="Maroon">A</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon">K</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E10:20_1_1_1_1_2_2"/><i><font color="Green">E117</font></i>: 
( <font color="Maroon">K</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E11:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon">C</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E13:20_1_1_1_1_2_2"/><i><font color="Green">E118</font></i>: 
( <font color="Maroon">C</font> is <a href="aff_1.html#V1">being_line</a> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33">AFF_1:33</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2"/>
 ex <font color="Olive">d1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Olive">d1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_3"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_1_1_2_2_3"/><i><font color="Green">E119</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_1_1_2_2_3"/><i><font color="Green">E120</font></i>: 
( <font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_3"/>
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_3_1"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</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#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_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">c</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E8:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_3_1"/><b>then </b><i><font color="Green">E122</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_3_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_3_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1_1_1_1_2_2_3_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_1_1_2_2_3"/><i><font color="Green">E123</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d1</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>,<font color="Maroon">d1</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d1</font>
;<br/>

<a NAME="E8:20_1_1_1_1_2_2_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">e1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_3"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_3"/>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:20_1_1_1_1_2_2_3"/>
( <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font> )
 <b>by </b><i>, , , , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E16:20_1_1_1_1_2_2"/><i><font color="Green">E125</font></i>: 
( <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font> )
 ;<br/><a NAME="E17:20_1_1_1_1_2_2"/>
 ex <font color="Olive">d2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Olive">d2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_4"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_1_1_2_2_4"/><i><font color="Green">E126</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_1_1_2_2_4"/><i><font color="Green">E127</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_4"/>
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_4_1"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<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="E6:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_4_1"/><b>then </b><i><font color="Green">E128</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_4_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_4_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_1_1_2_2_4_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_1_1_2_2_4"/><i><font color="Green">E129</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d2</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>,<font color="Maroon">d2</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d2</font>
;<br/>

<a NAME="E8:20_1_1_1_1_2_2_4"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">e1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_4"/><b>then </b><i><font color="Green">E130</font></i>: 
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_4"/>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:20_1_1_1_1_2_2_4"/>
( <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font> )
 <b>by </b><i>, , , , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E19:20_1_1_1_1_2_2"/><i><font color="Green">E131</font></i>: 
( <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font> )
 ;<br/><a NAME="E20:20_1_1_1_1_2_2"/>
 ex <font color="Olive">d3</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Olive">d3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_5"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_1_1_2_2_5"/><i><font color="Green">E132</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_1_1_2_2_5"/><i><font color="Green">E133</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_5"/>
not <font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_5_1"/>
<font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green">E134</font></i>: 
<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="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_5_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="E5:20_1_1_1_1_2_2_5_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="E6:20_1_1_1_1_2_2_5_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="E7:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green">E135</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="E8:20_1_1_1_1_2_2_5_1"/><i><font color="Green">E136</font></i>: 
( <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_5_1"/><b>then </b><i><font color="Green">E137</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_5_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_5_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">c1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_5_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">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_5_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E18:20_1_1_1_1_2_2_5_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d3</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_1_1_2_2_5"/><i><font color="Green">E138</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">e1</font>,<font color="Maroon">d3</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>,<font color="Maroon">d3</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d3</font>
;<br/>

<a NAME="E8:20_1_1_1_1_2_2_5"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">e1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_5"/><b>then </b><i><font color="Green">E139</font></i>: 
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_5"/>
<font color="Maroon">d1</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:20_1_1_1_1_2_2_5"/>
( <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font> )
 <b>by </b><i>, , , , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d3</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E22:20_1_1_1_1_2_2"/><i><font color="Green">E140</font></i>: 
( <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font> )
 ;<br/><a NAME="E23:20_1_1_1_1_2_2"/>
 ex <font color="Olive">d4</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Olive">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Olive">d4</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_1_1_2_2_6"/><i><font color="Green">E141</font></i>: 
( <font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_1_1_2_2_6"/><i><font color="Green">E142</font></i>: 
( <font color="Maroon">d1</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6"/>
not <font color="Maroon">b1</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon">b1</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green">E143</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green">E145</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green">E146</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_1_1"/><i><font color="Green">E147</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_1_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1_1_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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b><i><font color="Green">E148</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_1_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_6_1_1_1"/>
contradiction
 <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="E3:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green">E149</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</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#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</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="E8:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green">E150</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green">E151</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="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_6_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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_6_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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_6_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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green">E152</font></i>: 
<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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_6_1_1"/><i><font color="Green">E153</font></i>: 
( <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_6_1_1"/><b>then </b><i><font color="Green">E154</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_6_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</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="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_6_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">c1</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E19:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E20:20_1_1_1_1_2_2_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">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E22:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E24:20_1_1_1_1_2_2_6_1_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E25:20_1_1_1_1_2_2_6_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green">E155</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green">E156</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_6_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">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_6_1"/><b>then </b><i><font color="Green">E157</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">c1</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_6_1"/><i><font color="Green">E158</font></i>: 
<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="20_1_1_1_1_2_2_6_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_2"/><i><font color="Green">E159</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_2"/><i><font color="Green">E160</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_6_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E3:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b><i><font color="Green">E161</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_6_1_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_6_1_2"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2"/><b>then </b><i><font color="Green">E162</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_6_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b><i><font color="Green">E163</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</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/>
<a NAME="E7:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</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="E11:20_1_1_1_1_2_2_6_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">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1_1_1_1_2_2_6_1_2_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_6_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E15:20_1_1_1_1_2_2_6_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_6_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">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_6_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">c</font>
 
<b>by </b><i><a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_6_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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:20_1_1_1_1_2_2_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</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="E20:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E22:20_1_1_1_1_2_2_6_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E23:20_1_1_1_1_2_2_6_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d4</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_1_1_2_2_6"/><i><font color="Green">E164</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">e1</font>,<font color="Maroon">d4</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>,<font color="Maroon">d4</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d4</font>
;<br/>

<a NAME="E8:20_1_1_1_1_2_2_6"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">e1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_6"/><b>then </b><i><font color="Green">E165</font></i>: 
<font color="Maroon">e1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_6"/>
<font color="Maroon">d1</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:20_1_1_1_1_2_2_6"/>
( <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font> )
 <b>by </b><i>, , , , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d4</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E25:20_1_1_1_1_2_2"/><i><font color="Green">E166</font></i>: 
( <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font> )
 ;<br/><a NAME="E26:20_1_1_1_1_2_2"/><i><font color="Green">E167</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i>, , , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E27:20_1_1_1_1_2_2"/><i><font color="Green">E168</font></i>: 
( not <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7"/><i><font color="Green">E169</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/>

<div><i><font color="Green">E170</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_1"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green">E172</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="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_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#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_7_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#T15">AFF_1:15</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green">E173</font></i>: 
<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#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_1"/><b>then </b><i><font color="Green">E174</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">b1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_7_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_7_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">c1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E11:20_1_1_1_1_2_2_7_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">c1</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_7_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">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2_7_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E15:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E16:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E17:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E18:20_1_1_1_1_2_2_7_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E19:20_1_1_1_1_2_2_7_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E175</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2"/><i><font color="Green">E176</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_7_2"/>
<font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_7_2"/><b>then </b><i><font color="Green">E177</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_2"/><i><font color="Green">E178</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_1"/><b>then </b><i><font color="Green">E179</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:20_1_1_1_1_2_2_7_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_2"/><b>then </b><i><font color="Green">E180</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_2"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E6:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</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="E10:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E11:20_1_1_1_1_2_2_7_2"/><b>then </b><i><font color="Green">E181</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_7_2"/><i><font color="Green">E182</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="20_1_1_1_1_2_2_7_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_2_3"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_7_2_3"/><b>then </b><i><font color="Green">E183</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_2_3"/>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_2_3"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_2_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:20_1_1_1_1_2_2_7_2"/>
 <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="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E15:20_1_1_1_1_2_2_7_2"/><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">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E16:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E17:20_1_1_1_1_2_2_7_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</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="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E18:20_1_1_1_1_2_2_7_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E184</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_3"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_7_3"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_3_1"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_7_3_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_3_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_7_3_1"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_7_3_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_7_3_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_7_3_1"/>
contradiction
 <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="E3:20_1_1_1_1_2_2_7_3"/><i><font color="Green">E189</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_3"/>
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_7_3"/><b>then </b><i><font color="Green">E190</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_7_3"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_7_3"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_7_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">c1</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/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_7_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_4"/><i><font color="Green">E191</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_7_4"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_7_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_7_4_1"/><i><font color="Green">E193</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_7_4_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_7_4_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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_7_4_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_7_4_1"/><b>then </b><i><font color="Green">E194</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_7_4_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_7_4_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_7_4_1"/>
contradiction
 <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="E3:20_1_1_1_1_2_2_7_4"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_7_4"/>
<font color="Maroon">d</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_1_1_2_2_7_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_7"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E28:20_1_1_1_1_2_2"/><i><font color="Green">E196</font></i>: 
( not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8"/><i><font color="Green">E197</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<div><i><font color="Green">E198</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_1"/><i><font color="Green">E199</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_8_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_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">c</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E5:20_1_1_1_1_2_2_8_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_1"/><b>then </b><i><font color="Green">E200</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_8_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_8_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_8_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E201</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_2"/><i><font color="Green">E202</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_8_2"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_2"/><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">b</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_2"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_8_2"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_2"/><b>then </b><i><font color="Green">E203</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_8_2"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_8_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_8_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E204</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_3"/><i><font color="Green">E205</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_8_3"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_8_3"/><b>then </b><i><font color="Green">E206</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_8_3"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_8_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_8_3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E7:20_1_1_1_1_2_2_8_3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4"/><i><font color="Green">E207</font></i>: 
<font color="Maroon">d3</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_8_4"/><i><font color="Green">E208</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green">E209</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green">E210</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_8_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_8_4_1_1"/><i><font color="Green">E211</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_8_4_1_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_8_4_1_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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b><i><font color="Green">E212</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_8_4_1_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_8_4_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_1_1_2_2_8_4_1_1"/>
contradiction
 <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="E3:20_1_1_1_1_2_2_8_4_1"/><i><font color="Green">E213</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E214</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E215</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_8_4_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_8_4_1"/><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">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_8_4_1"/><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="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E216</font></i>: 
 <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="E12:20_1_1_1_1_2_2_8_4_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="E13:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E217</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="E14:20_1_1_1_1_2_2_8_4_1"/>
( <font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font> &amp; <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E218</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">b1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_8_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">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E19:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E20:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E21:20_1_1_1_1_2_2_8_4_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E22:20_1_1_1_1_2_2_8_4_1"/><b>then </b><i><font color="Green">E219</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E23:20_1_1_1_1_2_2_8_4_1"/>
 <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="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E24:20_1_1_1_1_2_2_8_4_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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E25:20_1_1_1_1_2_2_8_4_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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E26:20_1_1_1_1_2_2_8_4_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_1_1_2_2_8_4"/>
<font color="Maroon">d1</font>,<font color="Maroon">d3</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="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_8_4"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_8"/>
contradiction
 <b>by </b><i><a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a></i>;<br/>


</div><b>end;</b></div><a NAME="E29:20_1_1_1_1_2_2"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E30:20_1_1_1_1_2_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_9"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_9"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_9"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_9"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E31:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green">E221</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, , , , , , , , , <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, </i>;<br/><a NAME="E32:20_1_1_1_1_2_2"/><i><font color="Green">E222</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_10"/>
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_10_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_10_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_10_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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_10_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_1_1_2_2_10_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 <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="E2:20_1_1_1_1_2_2_10"/>
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div><a NAME="E33:20_1_1_1_1_2_2"/><i><font color="Green">E223</font></i>: 
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_11"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_11_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_11_1"/>
<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<b>hence </b><a NAME="E2:20_1_1_1_1_2_2_11_1"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <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="E2:20_1_1_1_1_2_2_11"/>
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><a NAME="E34:20_1_1_1_1_2_2"/><i><font color="Green">E224</font></i>: 
( not <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12"/><i><font color="Green">E225</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> or <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> or <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> or <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 ;<br/>

<div><i><font color="Green">E226</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon">K</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">K</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green">E228</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_12_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">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green">E229</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green">E230</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_12_1"/><b>then </b><i><font color="Green">E231</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">c1</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_12_1"/><i><font color="Green">E232</font></i>: 
<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="20_1_1_1_1_2_2_12_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green">E233</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green">E234</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_1"/><i><font color="Green">E235</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_1"/><i><font color="Green">E236</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b><i><font color="Green">E237</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b><i><font color="Green">E238</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</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="conmetr1.html#T3" target="_self">Th3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</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="E7:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</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="E8:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_12_1_1_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">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_12_1_1_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">b1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b><i><font color="Green">E239</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_12_1_1_1"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_12_1_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E15:20_1_1_1_1_2_2_12_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green">E54</font></i></a>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green">E240</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_1_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</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="E3:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b><i><font color="Green">E241</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1_2"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1"/><i><font color="Green">E242</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_12_1_1_3"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b><i><font color="Green">E243</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">o</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon">a</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="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="conmetr1.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E5:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</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="E6:20_1_1_1_1_2_2_12_1_1_3"/><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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_12_1_1_3"/><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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_12_1_1_3"/><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">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_12_1_1_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:20_1_1_1_1_2_2_12_1_1_3"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:20_1_1_1_1_2_2_12_1_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="conmetr1.html#T2" target="_self">Th2</a>, <a class="ref" href="conmetr1.html#T3" target="_self">Th3</a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/>


</div><b>end;</b></div><a NAME="E11:20_1_1_1_1_2_2_12_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_12_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">c1</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_12_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">c</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E14:20_1_1_1_1_2_2_12_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#D1">AFF_1:def 1</a></i>;<br/><a NAME="E15:20_1_1_1_1_2_2_12_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#T15">AFF_1:15</a></i>;<br/><a NAME="E16:20_1_1_1_1_2_2_12_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#D1">AFF_1:def 1</a></i>;<br/><a NAME="E17:20_1_1_1_1_2_2_12_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="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E18:20_1_1_1_1_2_2_12_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">b1</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E19:20_1_1_1_1_2_2_12_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E20:20_1_1_1_1_2_2_12_1"/>
contradiction
 <b>by </b><i>, , <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E244</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_2"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_12_2"/>
<font color="Maroon">K</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">K</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_2"/><b>then </b><i><font color="Green">E246</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</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="E6:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_12_2"/><b>then </b><i><font color="Green">E247</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_12_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, , <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E9:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E10:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E11:20_1_1_1_1_2_2_12_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E12:20_1_1_1_1_2_2_12_2"/><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">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E13:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E14:20_1_1_1_1_2_2_12_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</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="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E15:20_1_1_1_1_2_2_12_2"/>
contradiction
 <b>by </b><i>, , <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E248</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_3"/><i><font color="Green">E249</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_12_3"/><i><font color="Green">E250</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_3"/><i><font color="Green">E251</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_3_1"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_3_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_3_1"/><b>then </b><i><font color="Green">E253</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_3_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_3_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_3_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_3_1"/>
contradiction
 <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="E4:20_1_1_1_1_2_2_12_3"/>
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_3"/><b>then </b><i><font color="Green">E254</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/><a NAME="E6:20_1_1_1_1_2_2_12_3"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E7:20_1_1_1_1_2_2_12_3"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E8:20_1_1_1_1_2_2_12_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">c1</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/><b>hence </b><a NAME="E9:20_1_1_1_1_2_2_12_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_4"/><i><font color="Green">E255</font></i>: 
<font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_12_4"/><i><font color="Green">E256</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_12_4"/><i><font color="Green">E257</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_12_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_12_4_1"/><i><font color="Green">E258</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_12_4_1"/>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_12_4_1"/><b>then </b><i><font color="Green">E259</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_12_4_1"/>
<font color="Maroon">C</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_12_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_12_4_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E7:20_1_1_1_1_2_2_12_4_1"/>
contradiction
 <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="E4:20_1_1_1_1_2_2_12_4"/>
<font color="Maroon">d</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E5:20_1_1_1_1_2_2_12_4"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_1_1_2_2_12_4"/>
contradiction
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_12"/>
contradiction
 <b>by </b><i><a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E35:20_1_1_1_1_2_2"/><i><font color="Green">E260</font></i>: 
( not <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; not <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13"/><i><font color="Green">E261</font></i>: 
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> or <font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<div><i><font color="Green">E262</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_1"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_13_1"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_13_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c1</font>,<font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_13_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E264</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_2"/><i><font color="Green">E265</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_13_2"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_1_1_2_2_13_2"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_1_1_2_2_13_2"/>
contradiction
 <b>by </b><i>, , , <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_13_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_1_1_2_2_13_3"/><i><font color="Green">E266</font></i>: 
<font color="Maroon">d4</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:20_1_1_1_1_2_2_13_3"/>
<font color="Maroon">d1</font>,<font color="Maroon">d4</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E3:20_1_1_1_1_2_2_13_3"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T62">AFF_1:62</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_13"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E36:20_1_1_1_1_2_2"/><i><font color="Green">E267</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_14"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_14_1"/><i><font color="Green">E268</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_14_1"/><i><font color="Green">E269</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_14_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_14_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_1_1_2_2_14_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_1_1_1_1_2_2_14"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_14"/>
<font color="Maroon">a1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>


</div><b>end;</b></div><a NAME="E37:20_1_1_1_1_2_2"/><i><font color="Green">E270</font></i>: 
<font color="Maroon">c1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_15"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_15"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_15"/><b>then </b>
<font color="Maroon">c1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_15"/>
<font color="Maroon">c1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E38:20_1_1_1_1_2_2"/>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_1_1_2_2_16"/><i><font color="Green">E271</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">b1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T65">AFF_1:65</a></i>;<br/>
<a NAME="E2:20_1_1_1_1_2_2_16"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>
 
<b>by </b><i>, , , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_16"/>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d4</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E39:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green">E272</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="conmetr1.html#T1" target="_self">Th1</a>, <a class="txt" href="conmetr1.html#E1:20"><i><font color="Green">E45</font></i></a>, </i>;<br/><a NAME="E40:20_1_1_1_1_2_2"/><i><font color="Green">E273</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_17"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_17"/>
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_17"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">c1</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/>
<a NAME="E5:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon">a</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="E6:20_1_1_1_1_2_2_17"/><b>then </b><i><font color="Green">E274</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_17"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_17"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E9:20_1_1_1_1_2_2_17"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E41:20_1_1_1_1_2_2"/><i><font color="Green">E275</font></i>: 
<font color="Maroon">d4</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_18"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_18"/><i><font color="Green">E276</font></i>: 
<font color="Maroon">d4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_18"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_18_1"/><i><font color="Green">E277</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d3</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_18_1"/><i><font color="Green">E278</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 
<b>by </b><i>, , , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E3:20_1_1_1_1_2_2_18_1"/><i><font color="Green">E279</font></i>: 
( <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">A</font> &amp; <font color="Maroon">K</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">K</font> )
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_18_1"/><b>then </b><i><font color="Green">E280</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, , <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_18_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d3</font>
 
<b>by </b><i>, , <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="conmetr1.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_1_1_2_2_18_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="conmetr1.html#T3" target="_self">Th3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green">E281</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_1_1_2_2_18"/><i><font color="Green">E282</font></i>: 
( <font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font> &amp; <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/>
<a NAME="E5:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green">E283</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="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_1_1_2_2_18"/><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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_1_1_2_2_18"/><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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E10:20_1_1_1_1_2_2_18"/><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#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_1_1_2_2_18"/><b>then </b><i><font color="Green">E284</font></i>: 
<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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E12:20_1_1_1_1_2_2_18"/><i><font color="Green">E285</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">b1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font> )
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E2:20_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E13:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#T2" target="_self">Th2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E14:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E15:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E16:20_1_1_1_1_2_2_18"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E17:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E19:20_1_1_1_1_2_2_18"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E20:20_1_1_1_1_2_2_18"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#T3" target="_self">Th3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E42:20_1_1_1_1_2_2"/>
<font color="Maroon">d2</font>,<font color="Maroon">d3</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="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E43:20_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon">d2</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 <b>by </b><i>, <a class="txt" href="conmetr1.html#E1:20_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E44:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d2</font>,<font color="Maroon">d3</font>,<font color="Maroon">d4</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E45:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d4</font>,<font color="Maroon">d3</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E46:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green">E286</font></i>: 
<font color="Maroon">d4</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d4</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E47:20_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d3</font>,<font color="Maroon">d4</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E48:20_1_1_1_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d4</font>,<font color="Maroon">d3</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E49:20_1_1_1_1_2_2"/><b>then </b>
<font color="Maroon">d4</font>,<font color="Maroon">d3</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d4</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E50:20_1_1_1_1_2_2"/><b>then </b><i><font color="Green">E287</font></i>: 
<font color="Maroon">d4</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d4</font>,<font color="Maroon">d1</font>
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:20_1_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="conmetr1.html#E3:20_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E51:20_1_1_1_1_2_2"/>
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d4</font>,<font color="Maroon">d2</font>,<font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1_1_2_2_19"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_1_1_2_2_19"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d4</font>,<font color="Maroon">d2</font>,<font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_1_1_2_2_19"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d4</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_1_1_2_2_19"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="txt" href="conmetr1.html#E1:20_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E52:20_1_1_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:20_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_1_1_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:20_1_1_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>,<font color="Maroon">d</font> or <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font> )
 ;<br/></div><b>end;</b></div><div><i><font color="Green">E288</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_2"/>
<font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 ;<br/><a NAME="E2:20_1_1_2"/><b>then </b><i><font color="Green">E289</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <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#T59">AFF_1:59</a></i>;<br/><a NAME="E3:20_1_1_2"/>
<font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3"/><i><font color="Green">E290</font></i>: 
not <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 ;<br/><a NAME="E2:20_1_1_3"/><i><font color="Green">E291</font></i>: 
( <font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Z</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">M</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T55">AFF_1:55</a></i>;<br/><a NAME="E3:20_1_1_3"/><i><font color="Green">E292</font></i>: 
( not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_1"/><i><font color="Green">E293</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> or <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 ;<br/>

<div><i><font color="Green">E294</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:20_1_1_3_1_1"/><b>then </b><i><font color="Green">E295</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_3_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_3_1_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_3_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/><a NAME="E2:20_1_1_3_1_2"/><b>then </b><i><font color="Green">E296</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E3:20_1_1_3_1_2"/>
<font color="Maroon">o</font>,<font color="Maroon">a</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/><a NAME="E4:20_1_1_3_1_2"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/><b>hence </b><a NAME="E5:20_1_1_3_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20_1_1_3_1"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_3"/><i><font color="Green">E297</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">c</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="20_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2"/><i><font color="Green">E298</font></i>: 
(  not <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> or  not <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> or  not <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> )
 ;<br/>

<div><i><font color="Green">E299</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_1"/><i><font color="Green">E300</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font>
 ;<br/><a NAME="E2:20_1_1_3_2_1"/><i><font color="Green">E301</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:20_1_1_3_2_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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_2_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_2_1"/><i><font color="Green">E302</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">b1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E4:20_1_1_3_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E5:20_1_1_3_2_1"/><b>then </b><i><font color="Green">E303</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E6:20_1_1_3_2_1"/><i><font color="Green">E304</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2_1_2"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:20_1_1_3_2_1_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#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_2_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><a NAME="E7:20_1_1_3_2_1"/><i><font color="Green">E305</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E8:20_1_1_3_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</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="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E9:20_1_1_3_2_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E10:20_1_1_3_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E306</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_2"/><i><font color="Green">E307</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/><a NAME="E2:20_1_1_3_2_2"/><i><font color="Green">E308</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_3_2_2"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E4:20_1_1_3_2_2"/><b>then </b><i><font color="Green">E309</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_3_2_2"/>
<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="aff_1.html#T53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_3_2_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_2_3"/><i><font color="Green">E310</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 ;<br/><a NAME="E2:20_1_1_3_2_3"/><i><font color="Green">E311</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E3:20_1_1_3_2_3"/>
<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E4:20_1_1_3_2_3"/><b>then </b><i><font color="Green">E312</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_3_2_3"/>
<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="aff_1.html#T53">AFF_1:53</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1_3_2_3"/>
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>hence </b><a NAME="E5:20_1_1_3_2"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div><a NAME="E5:20_1_1_3"/><i><font color="Green">E313</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> &amp; <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3"/><i><font color="Green">E314</font></i>: 
(  not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> or  not <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> or  not <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> )
 ;<br/>

<div><i><font color="Green">E315</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_1"/><i><font color="Green">E316</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:20_1_1_3_3_1"/><i><font color="Green">E317</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_1"/><i><font color="Green">E318</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_1_1"/><i><font color="Green">E319</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_1_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_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="E3:20_1_1_3_3_1_1"/>
<font color="Maroon">b</font>,<font color="Maroon">o</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_1_1"/><b>then </b><i><font color="Green">E320</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_1_1"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_1_1_2"/><i><font color="Green">E321</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</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="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_1_1_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</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="E4:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">a</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="E5:20_1_1_3_3_1_1_2"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_3_3_1_1_2"/><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">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_1_1_2"/><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">b1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_3_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_3_3_1_1_2"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:20_1_1_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="E3:20_1_1_3_3_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_2"/><i><font color="Green">E322</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_1_2"/><i><font color="Green">E323</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_1_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_1_2_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#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_3_3_1_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:20_1_1_3_3_1_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_1_2"/><b>then </b><i><font color="Green">E324</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_1_2"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_1_2_2"/><i><font color="Green">E325</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c1</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#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_1_2_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</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#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:20_1_1_3_3_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#T15">AFF_1:15</a></i>;<br/>
<a NAME="E6:20_1_1_3_3_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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_1_2_2"/><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">a</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c1</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/>
<a NAME="E9:20_1_1_3_3_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_3_3_1_2_2"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c1</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>
<b>hence </b><a NAME="E6:20_1_1_3_3_1_2"/>
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>hence </b><a NAME="E4:20_1_1_3_3_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E326</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_2"/><i><font color="Green">E327</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:20_1_1_3_3_2"/><i><font color="Green">E328</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_2_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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_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="E3:20_1_1_3_3_2"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_3_3_2"/><b>then </b><i><font color="Green">E329</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_3_3_2"/>
<font color="Maroon">b</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_2_2"/><i><font color="Green">E330</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</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/>
<a NAME="E5:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</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/>
<a NAME="E6:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_2_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b</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="E9:20_1_1_3_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_3_3_2_2"/>
<font color="Maroon">b</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1_3_3_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_3_3"/><i><font color="Green">E331</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><a NAME="E2:20_1_1_3_3_3"/><i><font color="Green">E332</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_3_3_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_3_3_3_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#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_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="E3:20_1_1_3_3_3"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/><a NAME="E4:20_1_1_3_3_3"/><b>then </b><i><font color="Green">E333</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E5:20_1_1_3_3_3"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_3_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_3_3_2"/><i><font color="Green">E334</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E2:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">a</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="E5:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</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="E6:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E7:20_1_1_3_3_3_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E8:20_1_1_3_3_3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<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="E9:20_1_1_3_3_3_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">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_3_3_3_2"/>
<font color="Maroon">c</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1_3_3_3"/>
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>hence </b><a NAME="E5:20_1_1_3_3"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_3"/><i><font color="Green">E335</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><a NAME="E8:20_1_1_3"/><i><font color="Green">E336</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , , , </i>;<br/><a NAME="E9:20_1_1_3"/>
 ex <font color="Olive">d1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Olive">d1</font> &amp; <font color="Olive">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_4"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_3_4"/><i><font color="Green">E337</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">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_3_4"/><i><font color="Green">E338</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_3_4"/>
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_4_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_4_1"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_3_4_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_3_4_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">o</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="E6:20_1_1_3_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>
<b>then consider </b><font color="Maroon">d1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_3_4"/><i><font color="Green">E339</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d1</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>,<font color="Maroon">d1</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d1</font>
;<br/>

<a NAME="E8:20_1_1_3_4"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_4"/><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">d1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_3_4"/><b>then </b><i><font color="Green">E340</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b</font>,<font color="Maroon">d1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_3_4"/>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1_1_3_4"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E11:20_1_1_3"/><i><font color="Green">E341</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 ;<br/><a NAME="E12:20_1_1_3"/>
 ex <font color="Olive">d2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Olive">d2</font> &amp; <font color="Olive">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_5"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_3_5"/><i><font color="Green">E342</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_3_5"/><i><font color="Green">E343</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_3_5"/>
not <font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_5_1"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_5_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_5_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E4:20_1_1_3_5_1"/><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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E5:20_1_1_3_5_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">o</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="E6:20_1_1_3_5_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>
<b>then consider </b><font color="Maroon">d2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_3_5"/><i><font color="Green">E344</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">e1</font>,<font color="Maroon">d2</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">e2</font>,<font color="Maroon">d2</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d2</font>
;<br/>

<a NAME="E8:20_1_1_3_5"/>
<font color="Maroon">o</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_5"/><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">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E10:20_1_1_3_5"/><b>then </b><i><font color="Green">E345</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">c</font>,<font color="Maroon">d2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:20_1_1_3_5"/>
<font color="Maroon">d</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1_1_3_5"/>
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a>, <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">d2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E14:20_1_1_3"/><i><font color="Green">E346</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> )
 ;<br/><a NAME="E15:20_1_1_3"/><i><font color="Green">E347</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6"/>
<font color="Maroon">d1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_6"/><b>then </b><i><font color="Green">E348</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_6"/><i><font color="Green">E349</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6_1"/><i><font color="Green">E350</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_6_1"/><i><font color="Green">E351</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">a1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:20_1_1_3_6_1"/><i><font color="Green">E352</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_6_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_6_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_6_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="E3:20_1_1_3_6_1_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E4:20_1_1_3_6_1_1"/><b>then </b><i><font color="Green">E353</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E5:20_1_1_3_6_1_1"/>
<font color="Maroon">o</font>,<font color="Maroon">c</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<b>hence </b><a NAME="E6:20_1_1_3_6_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_6_1"/>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E8:20_1_1_3_6_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">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">o</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:20_1_1_3_6_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">o</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E11:20_1_1_3_6_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_3_6_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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E13:20_1_1_3_6_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="E4:20_1_1_3_6"/>
<font color="Maroon">o</font>,<font color="Maroon">d1</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_6"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>


</div><b>end;</b></div><div><i><font color="Green">E354</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_7"/><i><font color="Green">E355</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><a NAME="E2:20_1_1_3_7"/>
 ex <font color="Olive">d5</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font> st <br/>(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Olive">d5</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Olive">d5</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">e1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:20_1_1_3_7_1"/><i><font color="Green">E356</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">e1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e1</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<b>consider </b><font color="Maroon">e2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_3_7_1"/><i><font color="Green">E357</font></i>: 
( <font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font> &amp; <font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e2</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_1"/>
not <font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_1_1"/>
<font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_7_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">d5</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E7:20_1_1_3_7_1"/><i><font color="Green">E358</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">e1</font>,<font color="Maroon">d5</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">e2</font>,<font color="Maroon">d5</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon">d5</font>
;<br/>

<a NAME="E8:20_1_1_3_7_1"/>
( <font color="Maroon">d1</font>,<font color="Maroon">e2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d5</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">e1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d5</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_7_1"/><b>then </b>
( <font color="Maroon">d1</font>,<font color="Maroon">d2</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d5</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d5</font> )
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E10:20_1_1_3_7_1"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d5</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d5</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><b>then consider </b><font color="Maroon">d5</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:20_1_1_3_7"/><i><font color="Green">E359</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d5</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d5</font> )
 ;<br/><a NAME="E5:20_1_1_3_7"/><i><font color="Green">E360</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><div><i><font color="Green">E361</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_7_2"/><i><font color="Green">E362</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">d5</font>
 ;<br/><a NAME="E2:20_1_1_3_7_2"/><i><font color="Green">E363</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_1"/><b>then </b><i><font color="Green">E364</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">d</font>,<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="E3:20_1_1_3_7_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1_1"/><i><font color="Green">E365</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_1_1"/><b>then </b>
 <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="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E4:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E7:20_1_1_3_7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</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="E8:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:20_1_1_3_7_2_1_1"/><b>then </b><i><font color="Green">E366</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:20_1_1_3_7_2_1_1"/><i><font color="Green">E367</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="20_1_1_3_7_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_1_1_1"/><i><font color="Green">E368</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_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">a</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Maroon">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="E4:20_1_1_3_7_2_1_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.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="E11:20_1_1_3_7_2_1_1"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</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/>
<a NAME="E12:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E13:20_1_1_3_7_2_1_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</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="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E14:20_1_1_3_7_2_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_7_2_1"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_1"/><b>then </b><i><font color="Green">E369</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_1"/>
<font color="Maroon">o</font>,<font color="Maroon">b</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E7:20_1_1_3_7_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E8:20_1_1_3_7_2_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:20_1_1_3_7_2"/>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d5</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_7_2_2"/><i><font color="Green">E370</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<a NAME="E2:20_1_1_3_7_2_2"/><i><font color="Green">E371</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_2"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d5</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="E4:20_1_1_3_7_2_2"/>
<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">d5</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E5:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E6:20_1_1_3_7_2"/><b>then </b><i><font color="Green">E372</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E7:20_1_1_3_7_2"/><i><font color="Green">E373</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_3"/><i><font color="Green">E374</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_3"/><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="E3:20_1_1_3_7_2_3"/><b>then </b><i><font color="Green">E375</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="E4:20_1_1_3_7_2_3"/><i><font color="Green">E376</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">b1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_7_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_3_7_2_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_7_2_3"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_7_2_3"/><b>then </b><i><font color="Green">E377</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:20_1_1_3_7_2_3"/>
<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="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_3_7_2_3"/><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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_7_2_3"/><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">b1</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E14:20_1_1_3_7_2_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:20_1_1_3_7_2"/><i><font color="Green">E378</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_4"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_4"/><b>then </b><i><font color="Green">E379</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_4"/>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_4"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">Z</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_7_2_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:20_1_1_3_7_2"/><i><font color="Green">E380</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_7_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_5"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_5"/><b>then </b><i><font color="Green">E381</font></i>: 
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_5"/>
<font color="Maroon">o</font>,<font color="Maroon">d</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T66">AFF_1:66</a></i>;<br/>
<a NAME="E4:20_1_1_3_7_2_5"/><b>then </b>
<font color="Maroon">Y</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T67">AFF_1:67</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_3_7_2_5"/>
contradiction
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:20_1_1_3_7_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E11:20_1_1_3_7_2"/><b>then </b><i><font color="Green">E382</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E12:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E13:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E14:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E15:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</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="E16:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E17:20_1_1_3_7_2"/><b>then </b><i><font color="Green">E383</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E18:20_1_1_3_7_2"/><i><font color="Green">E384</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="20_1_1_3_7_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_7_2_6"/><i><font color="Green">E385</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_7_2_6"/>
<font color="Maroon">o</font>,<font color="Maroon">a1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_7_2_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</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="E4:20_1_1_3_7_2_6"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D6" target="_self">Def6</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:20_1_1_3_7_2"/>
 <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="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E20:20_1_1_3_7_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E21:20_1_1_3_7_2"/><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">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E22:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E23:20_1_1_3_7_2"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</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="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E24:20_1_1_3_7_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div><a NAME="E7:20_1_1_3_7"/>
not <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E8:20_1_1_3_7"/>
contradiction
 <b>by </b><i>, , , , , , , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1_1_3_8"/><i><font color="Green">E386</font></i>: 
not <font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>then consider </b><font color="Maroon">d5</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:20_1_1_3_8"/><i><font color="Green">E387</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">d5</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">d5</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74">AFF_1:74</a></i>;<br/><a NAME="E4:20_1_1_3_8"/><i><font color="Green">E388</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/><a NAME="E5:20_1_1_3_8"/><i><font color="Green">E389</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E6:20_1_1_3_8"/>
<font color="Maroon">a1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E7:20_1_1_3_8"/><b>then </b><i><font color="Green">E390</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">d</font>,<font color="Maroon">d5</font>
 <b>by </b><i>, , , , , , , , , </i>;<br/><a NAME="E8:20_1_1_3_8"/><i><font color="Green">E391</font></i>: 
not  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1"/>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_1"/><b>then </b><i><font color="Green">E392</font></i>: 
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">d</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1"/>
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1_1"/><i><font color="Green">E393</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1_1"/><b>then </b><i><font color="Green">E394</font></i>: 
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:20_1_1_3_8_1_1"/><i><font color="Green">E395</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">a1</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="20_1_1_3_8_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_1_1_1"/><i><font color="Green">E396</font></i>: 
(  not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> or  not <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font> )
 ;<br/>

<a NAME="E2:20_1_1_3_8_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">a</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Maroon">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="E4:20_1_1_3_8_1_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.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="E5:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_8_1_1"/><b>then </b>
 <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="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_3_8_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_8_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">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_8_1_1"/><b>then </b><i><font color="Green">E397</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E11:20_1_1_3_8_1_1"/>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 
<b>by </b><i>, , <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_8_1_1"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E14:20_1_1_3_8_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:20_1_1_3_8_1"/><b>then </b>
<font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , , <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>
<a NAME="E5:20_1_1_3_8_1"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_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">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="E7:20_1_1_3_8_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="E9:20_1_1_3_8"/>
<font color="Maroon">b1</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">d5</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3_8_2"/><i><font color="Green">E398</font></i>: 
<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c1</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T12">AFF_1:12</a></i>;<br/>
<a NAME="E2:20_1_1_3_8_2"/><i><font color="Green">E399</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">d5</font>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_2"/>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">d</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="E4:20_1_1_3_8_2"/>
<font color="Maroon">b1</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">d5</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:20_1_1_3_8"/><b>then </b>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d5</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T23">AFF_1:23</a></i>;<br/><a NAME="E11:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d</font>,<font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E12:20_1_1_3_8"/><b>then </b><i><font color="Green">E400</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">d1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E13:20_1_1_3_8"/><i><font color="Green">E401</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_3"/><i><font color="Green">E402</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_3"/><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="E3:20_1_1_3_8_3"/><b>then </b><i><font color="Green">E403</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="E4:20_1_1_3_8_3"/><i><font color="Green">E404</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">b1</font> &amp; <font color="Maroon">o</font>,<font color="Maroon">c</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E5:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E6:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon">o</font>,<font color="Maroon">b1</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="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<a NAME="E7:20_1_1_3_8_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E8:20_1_1_3_8_3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/>
<a NAME="E9:20_1_1_3_8_3"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:20_1_1_3_8_3"/><b>then </b><i><font color="Green">E405</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">o</font>,<font color="Maroon">b1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E11:20_1_1_3_8_3"/>
<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="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E12:20_1_1_3_8_3"/><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="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E13:20_1_1_3_8_3"/><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">b1</font>
 
<b>by </b><i>, <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E14:20_1_1_3_8_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:20_1_1_3_8"/><i><font color="Green">E406</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_4"/><i><font color="Green">E407</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_4"/>
<font color="Maroon">o</font>,<font color="Maroon">d</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_4"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</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="E4:20_1_1_3_8_4"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E15:20_1_1_3_8"/><i><font color="Green">E408</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_8_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_5"/><i><font color="Green">E409</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_5"/>
<font color="Maroon">o</font>,<font color="Maroon">d</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_5"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">d</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="E4:20_1_1_3_8_5"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="conmetr1.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="E16:20_1_1_3_8"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d2</font>
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D1" target="_self">Def1</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E17:20_1_1_3_8"/><b>then </b><i><font color="Green">E410</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E18:20_1_1_3_8"/><i><font color="Green">E411</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="20_1_1_3_8_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_8_6"/><i><font color="Green">E412</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 ;<br/>

<a NAME="E2:20_1_1_3_8_6"/>
<font color="Maroon">o</font>,<font color="Maroon">a1</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="aff_1.html#T53">AFF_1:53</a></i>;<br/>
<a NAME="E3:20_1_1_3_8_6"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">o</font>,<font color="Maroon">a1</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="E4:20_1_1_3_8_6"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:20_1_1_3_8"/>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i>, , <a class="ref" href="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E20:20_1_1_3_8"/><b>then </b>
<font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a1</font>,<font color="Maroon">c1</font>
 <b>by </b><i>, , <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/><a NAME="E21:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a1</font>,<font color="Maroon">b1</font>,<font color="Maroon">c1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E22:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b1</font>,<font color="Maroon">c1</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="E23:20_1_1_3_8"/><b>then </b>
<font color="Maroon">b1</font>,<font color="Maroon">c1</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b1</font>,<font color="Maroon">a1</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E24:20_1_1_3_8"/><b>then </b><i><font color="Green">E413</font></i>: 
<font color="Maroon">b1</font>,<font color="Maroon">c1</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="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E25:20_1_1_3_8"/>
 <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="conmetr1.html#D3" target="_self">Def3</a>, <a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E26:20_1_1_3_8"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15">AFF_1:15</a></i>;<br/><a NAME="E27:20_1_1_3_8"/><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">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/><a NAME="E28:20_1_1_3_8"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</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="E29:20_1_1_3_8"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">c</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="aff_1.html#T14">AFF_1:14</a></i>;<br/><b>hence </b><a NAME="E30:20_1_1_3_8"/>
contradiction
 <b>by </b><i>, <a class="ref" href="conmetr1.html#D4" target="_self">Def4</a>, <a class="ref" href="conmetr1.html#D5" target="_self">Def5</a>, <a class="ref" href="aff_1.html#T14">AFF_1:14</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E18:20_1_1_3"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:20_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">X</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a> 
 <b>by </b><i><a class="ref" href="aff_2.html#D4">AFF_2:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20"/>
( <font color="Maroon">X</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a>  implies <font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_2"/><i><font color="Green">E414</font></i>: 
<font color="Maroon">X</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a> 
 ;<br/>

<a NAME="E2:20_2"/><b>then </b>
<font color="Maroon">X</font> <a href="aff_2.html#NR7" target="_self">satisfies_TDES</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T26">AFF_2:26</a></i>;<br/>
<a NAME="E3:20_2"/><b>then </b>
<font color="Maroon">X</font> <a href="aff_2.html#NR8" target="_self">satisfies_TDES_1</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T17">AFF_2:17</a></i>;<br/>
<a NAME="E4:20_2"/><b>then </b>
<font color="Maroon">X</font> <a href="aff_2.html#NR12" target="_self">satisfies_des_1</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T27">AFF_2:27</a></i>;<br/>
<a NAME="E5:20_2"/><b>then </b>
<font color="Maroon">X</font> <a href="aff_2.html#NR11" target="_self">satisfies_des</a> 
 
<b>by </b><i><a class="ref" href="aff_2.html#T21">AFF_2:21</a></i>;<br/>
<a NAME="E6:20_2"/><b>then </b><i><font color="Green">E415</font></i>: 
<font color="Maroon">X</font> <a href="conmetr1.html#NR1" target="_self">satisfies_minor_SCH</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:20_2"/>
<font color="Maroon">X</font> <a href="conmetr1.html#NR2" target="_self">satisfies_major_SCH</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:20_2"/>
<font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a> 
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">X</font> <a href="aff_2.html#NR4" target="_self">satisfies_DES</a>  iff <font color="Maroon">X</font> <a href="conmetr1.html#NR3" target="_self">satisfies_SCH</a>  )
 <b>by </b><i/>;<br/>


</div>
