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<b>let </b><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>;<br/><b>let </b><font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c9">K</font>, <font color="Maroon" title="c10">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:98"/><i><font color="Green" title="E71">A1</font></i>: 
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">K</font>
 <b>and </b><br/><a NAME="E2:98"/><i><font color="Green" title="E72">A2</font></i>: 
<font color="Maroon" title="c10">N</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">K</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c11">p1</font>, <font color="Maroon" title="c12">q1</font>, <font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c14">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><b> such that </b><br/><a NAME="E4:98"/><i><font color="Green" title="E73">A3</font></i>: 
( <font color="Maroon" title="c11">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">q1</font> &amp; <font color="Maroon" title="c13">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">b</font> &amp; <font color="Maroon" title="c9">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c12">q1</font> &amp; <font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font> )
 <b>and </b><br/><a NAME="E5:98"/><i><font color="Green" title="E74">A4</font></i>: 
<font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c12">q1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:98"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="analmetr.html#T63" target="_self" title="ANALMETR:th.63">Th63</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">p2</font>, <font color="Maroon" title="c16">q2</font>, <font color="Maroon" title="c17">c</font>, <font color="Maroon" title="c18">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font><b> such that </b><br/><a NAME="E7:98"/><i><font color="Green" title="E75">A5</font></i>: 
( <font color="Maroon" title="c15">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">q2</font> &amp; <font color="Maroon" title="c17">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">d</font> &amp; <font color="Maroon" title="c9">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">q2</font> &amp; <font color="Maroon" title="c10">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c17">c</font>,<font color="Maroon" title="c18">d</font> )
 <b>and </b><br/><a NAME="E8:98"/><i><font color="Green" title="E76">A6</font></i>: 
<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">q2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c17">c</font>,<font color="Maroon" title="c18">d</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:98"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="analmetr.html#T63" target="_self" title="ANALMETR:th.63">Th63</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c19">p1'</font> = <font color="Maroon" title="c11">p1</font>, <font color="Maroon" title="c20">p2'</font> = <font color="Maroon" title="c15">p2</font>, <font color="Maroon" title="c21">q1'</font> = <font color="Maroon" title="c12">q1</font>, <font color="Maroon" title="c22">q2'</font> = <font color="Maroon" title="c16">q2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c7">POS</font></span>)</span> ;<br/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font> = 
 <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">q2</font>
<b>by </b><i><a class="txt" href="analmetr.html#E4:98"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="analmetr.html#E7:98"><i><font color="Green" title="E75">A5</font></i></a>, <a class="ref" href="analmetr.html#T56" target="_self" title="ANALMETR:th.56">Th56</a></i>
<br/>.= 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c20">p2'</font>,<font color="Maroon" title="c22">q2'</font>
<b>by </b><i><a class="ref" href="analmetr.html#T56" target="_self" title="ANALMETR:th.56">Th56</a></i>
;<br/>
<a NAME="E11:98"/><b>then </b>
( <font color="Maroon" title="c20">p2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font> &amp; <font color="Maroon" title="c22">q2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/>
<a NAME="E12:98"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font>,<font color="Maroon" title="c20">p2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font>,<font color="Maroon" title="c22">q2'</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E13:98"/><b>then </b>
<font color="Maroon" title="c19">p1'</font>,<font color="Maroon" title="c21">q1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">p2'</font>,<font color="Maroon" title="c22">q2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/>
<a NAME="E14:98"/><b>then </b>
<font color="Maroon" title="c11">p1</font>,<font color="Maroon" title="c12">q1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">q2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E15:98"/><b>then </b>
<font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c16">q2</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E4:98"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="analmetr.html#E5:98"><i><font color="Green" title="E74">A4</font></i></a>, <a class="ref" href="analmetr.html#T84" target="_self" title="ANALMETR:th.84">Th84</a></i>;<br/>
<a NAME="E16:98"/><b>then </b>
<font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">c</font>,<font color="Maroon" title="c18">d</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E7:98"><i><font color="Green" title="E75">A5</font></i></a>, <a class="txt" href="analmetr.html#E8:98"><i><font color="Green" title="E76">A6</font></i></a>, <a class="ref" href="analmetr.html#T85" target="_self" title="ANALMETR:th.85">Th85</a></i>;<br/>
<b>hence </b><a NAME="E17:98"/>
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E4:98"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="analmetr.html#E7:98"><i><font color="Green" title="E75">A5</font></i></a>, <a class="ref" href="analmetr.html#D16" target="_self" title="ANALMETR:def.16">Def16</a></i>;<br/>


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