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<b>let </b><font color="Maroon">MS</font> be   <a href="analmetr.html#NM2">OrtAfPl</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">d1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>, <font color="Maroon">d2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">MS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E34</font></i>: 
not  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">d1</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> )
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">d2</font>,<font color="Maroon">a</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">d2</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> )
 ;<br/>

<b>assume </b><a NAME="E4:13"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">d1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font>
 ;<br/>

<a NAME="E5:13"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:13"/><b>then </b><i><font color="Green">E64</font></i>: 
( <font color="Maroon">d1</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">a</font> &amp; <font color="Maroon">d1</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2</font>,<font color="Maroon">b</font> )
 
<b>by </b><i>, , <a class="ref" href="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font>, <font color="Maroon">c'</font> = <font color="Maroon">c</font>, <font color="Maroon">d1'</font> = <font color="Maroon">d1</font>, <font color="Maroon">d2'</font> = <font color="Maroon">d2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">MS</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<a NAME="E8:13"/>
( <font color="Maroon">d1'</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">a'</font> &amp; <font color="Maroon">d1'</font>,<font color="Maroon">b'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d2'</font>,<font color="Maroon">b'</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:13"/><b>then </b>
( <font color="Maroon">a'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">d2'</font> &amp; <font color="Maroon">b'</font>,<font color="Maroon">d1'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">d2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/>
<a NAME="E10:13"/><b>then </b>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">d1'</font>,<font color="Maroon">d2'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">d1'</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="E11:13"/><b>then </b><i><font color="Green">E66</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">a'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</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="E12:13"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">d1'</font>,<font color="Maroon">d2'</font>,<font color="Maroon">d2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E13:13"/><b>then </b><i><font color="Green">E67</font></i>: 
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">d1'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">d2'</font> )
 
<b>by </b><i><a class="ref" href="euclmetr.html#D1" target="_self">Def1</a>, , <a class="ref" href="aff_1.html#T17">AFF_1:17</a></i>;<br/>
<b>set </b><font color="Maroon">X'</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>;<br/>
<a NAME="E14:13"/><i><font color="Green">E69</font></i>: 
(  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> &amp; <font color="Maroon">b'</font> <a href="hidden.html#R2">in</a>  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> )
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D3">AFF_1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">X</font> =  <a href="aff_1.html#K2">Line</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">MS</font> <b>by </b><i><a class="ref" href="analmetr.html#T57">ANALMETR:57</a></i>;<br/>
<a NAME="E16:13"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">d1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">d2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="analmetr.html#NR6" target="_self">is_line</a>  )
 
<b>by </b><i>, , <a class="ref" href="euclmetr.html#D2" target="_self">Def2</a>, <a class="ref" href="aff_1.html#T39">AFF_1:39</a>, <a class="ref" href="analmetr.html#T58">ANALMETR:58</a></i>;<br/>
<a NAME="E17:13"/>
( ( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font> ) &amp; ( <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d1</font> or <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d2</font> ) )
 
<b>by </b><i><a class="ref" href="euclmetr.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E18:13"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analmetr.html#R6">_|_</a> <font color="Maroon">X</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="analmetr.html#R6">_|_</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, , <a class="ref" href="euclmetr.html#D3" target="_self">Def3</a>, <a class="ref" href="analmetr.html#T77">ANALMETR:77</a></i>;<br/>
<a NAME="E19:13"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 
<b>by </b><i/>;<br/>
<a NAME="E20:13"/><b>then </b>
<font color="Maroon">a'</font>,<font color="Maroon">c'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">b'</font>,<font color="Maroon">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48">ANALMETR:48</a></i>;<br/>
<a NAME="E21:13"/><b>then </b>
<font color="Maroon">c'</font>,<font color="Maroon">b'</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="E22:13"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1">AFF_1:def 1</a></i>;<br/>
<a NAME="E23:13"/><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/>
<b>hence </b><a NAME="E24:13"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>


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