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<b>let </b><font color="Maroon">POS</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">POS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font>;<br/>









<b>assume </b><a NAME="E1:100"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 ;<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">d'</font> = <font color="Maroon">d</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" target="_self">Af</a> <font color="Maroon">POS</font></span>)</span> ;<br/>
<a NAME="E3:100"/>
(  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<font color="Maroon">c'</font> &amp;  <a href="aff_1.html#R1">LIN</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">a'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T16">AFF_1:16</a></i>;<br/>
<a NAME="E4:100"/><b>then </b><i><font color="Green">E39</font></i>: 
(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E12"><i><font color="Green">Lemma54</font></i></a></i>;<br/>
<div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:100_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:100_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/>;<br/><a NAME="E3:100_1"/><b>then </b>
 <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E6:100"><i><font color="Green">E51</font></i></a></i>;<br/><b>hence </b><a NAME="E4:100_1"/>
 ex <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Olive">p</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Olive">p</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="100_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:100_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><a NAME="E2:100_2"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">a</font>
 <b>by </b><i/>;<br/><a NAME="E3:100_2"/><b>then </b>
 <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E6:100"><i><font color="Green">E51</font></i></a></i>;<br/><b>hence </b><a NAME="E4:100_2"/>
 ex <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Olive">p</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Olive">p</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:100_3"/><i><font color="Green">E52</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">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 ;<br/><b>set </b><font color="Maroon">M</font> =  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><b>set </b><font color="Maroon">N</font> =  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>;<br/><a NAME="E2:100_3"/>
 <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="analmetr.html#R10" target="_self">_|_</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , </i>;<br/><b>then consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font><b> such that </b><br/><a NAME="E4:100_3"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> )
 <b>by </b><i/>;<br/><a NAME="E5:100_3"/>
(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">p</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T14" target="_self">Th14</a>, <a class="txt" href="analmetr.html#E1:100_3"><i><font color="Green">E52</font></i></a></i>;<br/><b>hence </b><a NAME="E6:100_3"/>
 ex <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Olive">p</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Olive">p</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:100"/>
 ex <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">POS</font> st <br/>(  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Olive">p</font> &amp;  <a href="analmetr.html#R5" target="_self">LIN</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Olive">p</font> )
 <b>by </b><i>, </i>;<br/>


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