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<b>let </b><font color="Maroon" title="c1">MS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>;<br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">c1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> )
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green" title="E33">A2</font></i>: 
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> )
 <b>and </b><br/><a NAME="E3:35"/><i><font color="Green" title="E34">A3</font></i>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> )
 <b>and </b><br/><a NAME="E4:35"/><i><font color="Green" title="E35">A4</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font>
 ;<br/>

<a NAME="E5:35"/><i><font color="Green" title="E36">A5</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ;<br/>

<a NAME="E2:35_1"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="euclmetr.html#E1:35"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="euclmetr.html#E2:35"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="euclmetr.html#E4:35"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:35_1"/><b>then </b>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:35_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:35_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="ref" href="euclmetr.html#T4" target="_self" title="EUCLMETR:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E6:35_1"/>
contradiction
 <b>by </b><i><a class="txt" href="euclmetr.html#E3:35"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:35"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c1</font>
 ;<br/>

<a NAME="E2:35_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="euclmetr.html#E1:35"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="euclmetr.html#E2:35"><i><font color="Green" title="E33">A2</font></i></a>, <a class="txt" href="euclmetr.html#E4:35"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:35_2"/><b>then </b>
<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E4:35_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:35_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="euclmetr.html#T4" target="_self" title="EUCLMETR:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E6:35_2"/>
contradiction
 <b>by </b><i><a class="txt" href="euclmetr.html#E3:35"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:35"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <b>by </b><i><a class="txt" href="euclmetr.html#E5:35"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="analmetr.html#T80" title="ANALMETR:th.80">ANALMETR:80</a></i>;<br/>


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