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<b>let </b><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a>;<br/><b>let </b><font color="Maroon" title="c8">M</font>, <font color="Maroon" title="c9">N</font>, <font color="Maroon" title="c10">K</font>, <font color="Maroon" title="c11">A</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>let </b><font color="Maroon" title="c12">p</font>, <font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c14">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:90"/><i><font color="Green" title="E66">A1</font></i>: 
( <font color="Maroon" title="c12">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c12">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c13">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c14">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">N</font> )
 <b>and </b><br/><a NAME="E2:90"/><i><font color="Green" title="E67">A2</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:90"/><i><font color="Green" title="E68">A3</font></i>: 
( <font color="Maroon" title="c13">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> &amp; <font color="Maroon" title="c14">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font> )
 <b>and </b><br/><a NAME="E4:90"/><i><font color="Green" title="E69">A4</font></i>: 
( <font color="Maroon" title="c11">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c11">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font> )
 <b>and </b><br/><a NAME="E5:90"/><i><font color="Green" title="E70">A5</font></i>: 
<font color="Maroon" title="c10">K</font> <a href="analmetr.html#NR6" title="ANALMETR:NR.6">is_line</a> 
 ;<br/>

<a NAME="E6:90"/><i><font color="Green" title="E71">A6</font></i>: 
<font color="Maroon" title="c10">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="c13">a</font>,<font color="Maroon" title="c14">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E2:90"><i><font color="Green" title="E67">A2</font></i></a>, <a class="txt" href="analmetr.html#E3:90"><i><font color="Green" title="E68">A3</font></i></a>, <a class="txt" href="analmetr.html#E5:90"><i><font color="Green" title="E70">A5</font></i></a>, <a class="ref" href="analmetr.html#T76" target="_self" title="ANALMETR:th.76">Th76</a></i>;<br/>
<a NAME="E7:90"/>
<font color="Maroon" title="c11">A</font> <a href="analmetr.html#NR6" title="ANALMETR:NR.6">is_line</a> 
 
<b>by </b><i><a class="txt" href="analmetr.html#E4:90"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="analmetr.html#T62" target="_self" title="ANALMETR:th.62">Th62</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c15">q</font>, <font color="Maroon" title="c16">r</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="E9:90"/><i><font color="Green" title="E72">A7</font></i>: 
( <font color="Maroon" title="c15">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">r</font> &amp; <font color="Maroon" title="c11">A</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">q</font>,<font color="Maroon" title="c16">r</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D13" target="_self" title="ANALMETR:def.13">Def13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">q'</font> = <font color="Maroon" title="c15">q</font>, <font color="Maroon" title="c18">r'</font> = <font color="Maroon" title="c16">r</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 NAME="E11:90"/>
 <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c15">q</font>,<font color="Maroon" title="c16">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c17">q'</font>,<font color="Maroon" title="c18">r'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56" target="_self" title="ANALMETR:th.56">Th56</a></i>;<br/>
<a NAME="E12:90"/><b>then </b>
( <font color="Maroon" title="c15">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A</font> &amp; <font color="Maroon" title="c16">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E9:90"><i><font color="Green" title="E72">A7</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/>
<a NAME="E13:90"/><b>then </b>
( <font color="Maroon" title="c15">q</font>,<font color="Maroon" title="c16">r</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c13">a</font> &amp; <font color="Maroon" title="c15">q</font>,<font color="Maroon" title="c16">r</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">p</font>,<font color="Maroon" title="c14">b</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:90"><i><font color="Green" title="E66">A1</font></i></a>, <a class="txt" href="analmetr.html#E4:90"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="analmetr.html#T78" target="_self" title="ANALMETR:th.78">Th78</a></i>;<br/>
<a NAME="E14:90"/><b>then </b>
<font color="Maroon" title="c15">q</font>,<font color="Maroon" title="c16">r</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="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E15:90"/>
<font color="Maroon" title="c11">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">K</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E2:90"><i><font color="Green" title="E67">A2</font></i></a>, <a class="txt" href="analmetr.html#E6:90"><i><font color="Green" title="E71">A6</font></i></a>, <a class="txt" href="analmetr.html#E9:90"><i><font color="Green" title="E72">A7</font></i></a>, <a class="ref" href="analmetr.html#T63" target="_self" title="ANALMETR:th.63">Th63</a></i>;<br/>


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