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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> 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="c10">a</font>, <font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c12">c</font>, <font color="Maroon" title="c13">d</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="E1:89"/><i><font color="Green" title="E68">A1</font></i>: 
( <font color="Maroon" title="c10">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="c11">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font> )
 <b>and </b><br/><a NAME="E2:89"/><i><font color="Green" title="E69">A2</font></i>: 
( <font color="Maroon" title="c12">c</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">d</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="E3:89"/><i><font color="Green" title="E70">A3</font></i>: 
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c14">p1</font>, <font color="Maroon" title="c15">q1</font>, <font color="Maroon" title="c16">p2</font>, <font color="Maroon" title="c17">q2</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="E5:89"/><i><font color="Green" title="E71">A4</font></i>: 
( <font color="Maroon" title="c14">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">q1</font> &amp; <font color="Maroon" title="c16">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">q2</font> )
 <b>and </b><br/><a NAME="E6:89"/><i><font color="Green" title="E72">A5</font></i>: 
( <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="c14">p1</font>,<font color="Maroon" title="c15">q1</font> &amp; <font color="Maroon" title="c9">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="c16">p2</font>,<font color="Maroon" title="c17">q2</font> &amp; <font color="Maroon" title="c14">p1</font>,<font color="Maroon" title="c15">q1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font> )
 <b>by </b><i><a class="txt" href="analmetr.html#E3:89"><i><font color="Green" title="E70">A3</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="c18">a'</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c19">b'</font> = <font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c20">c'</font> = <font color="Maroon" title="c12">c</font>, <font color="Maroon" title="c21">d'</font> = <font color="Maroon" title="c13">d</font>, <font color="Maroon" title="c22">p1'</font> = <font color="Maroon" title="c14">p1</font>, <font color="Maroon" title="c23">q1'</font> = <font color="Maroon" title="c15">q1</font>, <font color="Maroon" title="c24">p2'</font> = <font color="Maroon" title="c16">p2</font>, <font color="Maroon" title="c25">q2'</font> = <font color="Maroon" title="c17">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 NAME="E8:89"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">p1</font>,<font color="Maroon" title="c15">q1</font>,<font color="Maroon" title="c10">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">p1</font>,<font color="Maroon" title="c15">q1</font>,<font color="Maroon" title="c11">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font>,<font color="Maroon" title="c12">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font>,<font color="Maroon" title="c13">d</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:89"><i><font color="Green" title="E68">A1</font></i></a>, <a class="txt" href="analmetr.html#E2:89"><i><font color="Green" title="E69">A2</font></i></a>, <a class="txt" href="analmetr.html#E6:89"><i><font color="Green" title="E72">A5</font></i></a>, <a class="ref" href="analmetr.html#D12" target="_self" title="ANALMETR:def.12">Def12</a></i>;<br/>
<a NAME="E9:89"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">p1'</font>,<font color="Maroon" title="c23">q1'</font>,<font color="Maroon" title="c18">a'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">p1'</font>,<font color="Maroon" title="c23">q1'</font>,<font color="Maroon" title="c19">b'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">p2'</font>,<font color="Maroon" title="c25">q2'</font>,<font color="Maroon" title="c20">c'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">p2'</font>,<font color="Maroon" title="c25">q2'</font>,<font color="Maroon" title="c21">d'</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" target="_self" title="ANALMETR:th.55">Th55</a></i>;<br/>
<a NAME="E10:89"/><b>then </b>
( <font color="Maroon" title="c22">p1'</font>,<font color="Maroon" title="c23">q1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">a'</font>,<font color="Maroon" title="c19">b'</font> &amp; <font color="Maroon" title="c24">p2'</font>,<font color="Maroon" title="c25">q2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c21">d'</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="E11:89"/><b>then </b><i><font color="Green" title="E73">A6</font></i>: 
( <font color="Maroon" title="c14">p1</font>,<font color="Maroon" title="c15">q1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> &amp; <font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">c</font>,<font color="Maroon" title="c13">d</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" target="_self" title="ANALMETR:th.48">Th48</a></i>;<br/>
<a NAME="E12:89"/><b>then </b>
<font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E5:89"><i><font color="Green" title="E71">A4</font></i></a>, <a class="txt" href="analmetr.html#E6:89"><i><font color="Green" title="E72">A5</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E13:89"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">c</font>,<font color="Maroon" title="c13">d</font>
 <b>by </b><i><a class="txt" href="analmetr.html#E5:89"><i><font color="Green" title="E71">A4</font></i></a>, <a class="txt" href="analmetr.html#E11:89"><i><font color="Green" title="E73">A6</font></i></a>, <a class="ref" href="analmetr.html#D9" target="_self" title="ANALMETR:def.9">Def9</a></i>;<br/>


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