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

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font>, <font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:3"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:3"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>
<b>consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E6:3"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">p</font>,<font color="Maroon">c</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp;  <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T91">ANALMETR:91</a></i>;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>take </b>
<font color="Maroon">c</font>
;<br/>

<b>thus </b><a NAME="E7:3"/>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E8:3"/>
<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="3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:3_1"/>
not <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:3_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div>

<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">p'</font> = <font color="Maroon">p</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3">Af</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47">ANALMETR:47</a></i>;<br/>
<b>thus </b><a NAME="E10:3"/>
<font color="Maroon">b</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="3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:3_2"/>
not <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E2:3_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</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="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E3:3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">p</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">p'</font>,<font color="Maroon">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:3_2"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p'</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="E6:3_2"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:3_2"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E8:3_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:3_2"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E10:3_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E11:3"/>
not <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E12:3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<a NAME="E13:3"/><b>then </b>
<font color="Maroon">p</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="analmetr.html#T85">ANALMETR:85</a></i>;<br/>
<a NAME="E14:3"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">p</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="analmetr.html#T81">ANALMETR:81</a></i>;<br/>
<a NAME="E15:3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">b</font>,<font color="Maroon">p</font>,<font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">b'</font>,<font color="Maroon">p'</font>,<font color="Maroon">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:3"/><b>then </b>
 <a href="aff_1.html#R1">LIN</a> <font color="Maroon">p'</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="E18:3"/><b>then </b>
 <a href="analmetr.html#R5">LIN</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:3"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">p</font>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T84">ANALMETR:84</a></i>;<br/>
<a NAME="E21:3"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analmetr.html#R4">_|_</a> <font color="Maroon">a</font>,<font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83">ANALMETR:83</a></i>;<br/>
<b>hence </b><a NAME="E22:3"/>
contradiction
 <b>by </b><i>, <a class="ref" href="analmetr.html#T51">ANALMETR:51</a></i>;<br/>


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