<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">POS</font> be   <a href="analmetr.html#NM1" title="ANALMETR:NM.1">OrtAfSp</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">POS</font><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Olive" title="b5">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b6">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b1">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b2">N</font> holds <br/><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font></span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c7">POS</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Olive" title="b4">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font></span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font> &amp; <font color="Maroon" title="c12">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c13">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font> &amp; <font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font> implies <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> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:88"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font>
 <span class="kw">and </span><br/><a NAME="E2:88"/><span class="lab"><font color="Green" title="E60">A2</font></span>: 
<font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">M</font>
 <span class="kw">and </span><br/><a NAME="E3:88"/><span class="lab"><font color="Green" title="E61">A3</font></span>: 
<font color="Maroon" title="c12">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font>
 <span class="kw">and </span><br/><a NAME="E4:88"/><span class="lab"><font color="Green" title="E62">A4</font></span>: 
<font color="Maroon" title="c13">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">N</font>
 <span class="kw">and </span><br/><a NAME="E5:88"/><span class="lab"><font color="Green" title="E63">A5</font></span>: 
<font color="Maroon" title="c8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c9">N</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E7:88"/><span class="lab"><font color="Green" title="E64">A6</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:88"/><span class="lab"><font color="Green" title="E65">A7</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:88"/><span class="lab"><font color="Green" title="E66">A8</font></span>: 
<font color="Maroon" title="c8">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c14">p1</font>,<font color="Maroon" title="c15">q1</font>)
 <span class="kw">and </span><br/><a NAME="E10:88"/><span class="lab"><font color="Green" title="E67">A9</font></span>: 
<font color="Maroon" title="c9">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K3" title="ANALMETR:func.3">Line</a> (<font color="Maroon" title="c16">p2</font>,<font color="Maroon" title="c17">q2</font>)
 <span class="kw">and </span><br/><a NAME="E11:88"/><span class="lab"><font color="Green" title="E68">A10</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:88"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="ref" href="analmetr.html#T45" target="_self" onmouseover="rs('analmetr/T45')" onmouseout="rh()">Th45</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">a9</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c19">b9</font> = <font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c20">c9</font> = <font color="Maroon" title="c12">c</font>, <font color="Maroon" title="c21">d9</font> = <font color="Maroon" title="c13">d</font>, <font color="Maroon" title="c22">p19</font> = <font color="Maroon" title="c14">p1</font>, <font color="Maroon" title="c23">q19</font> = <font color="Maroon" title="c15">q1</font>, <font color="Maroon" title="c24">p29</font> = <font color="Maroon" title="c16">p2</font>, <font color="Maroon" title="c25">q29</font> = <font color="Maroon" title="c17">q2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">POS</font>, the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c7">POS</font> #) ;<br/>
<a NAME="E13:88"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88"><span class="lab"><font color="Green" title="E60">A2</font></span></a>, <a class="txt" href="#E9:88"><span class="lab"><font color="Green" title="E66">A8</font></span></a>, <a class="ref" href="analmetr.html#D11" target="_self" onmouseover="rs('analmetr/D11')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E14:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A11</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">q19</font>,<font color="Maroon" title="c19">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" target="_self" onmouseover="rs('analmetr/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<a NAME="E15:88"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="txt" href="#E9:88"><span class="lab"><font color="Green" title="E66">A8</font></span></a>, <a class="ref" href="analmetr.html#D11" target="_self" onmouseover="rs('analmetr/D11')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E16:88"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">q19</font>,<font color="Maroon" title="c18">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" target="_self" onmouseover="rs('analmetr/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<a NAME="E17:88"/><span class="kw">then </span>
<font color="Maroon" title="c22">p19</font>,<font color="Maroon" title="c23">q19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">a9</font>,<font color="Maroon" title="c19">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:88"><span class="lab"><font color="Green" title="E69">A11</font></span></a>, <a class="ref" href="aff_1.html#T10" onmouseover="rs('aff_1/T10')" onmouseout="rh()">AFF_1:10</a></span>;<br/>
<a NAME="E18:88"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E19:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A12</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:88"><span class="lab"><font color="Green" title="E64">A6</font></span></a>, <a class="txt" href="#E11:88"><span class="lab"><font color="Green" title="E68">A10</font></span></a>, <a class="ref" href="analmetr.html#D8" target="_self" onmouseover="rs('analmetr/D8')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E20:88"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:88"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="txt" href="#E10:88"><span class="lab"><font color="Green" title="E67">A9</font></span></a>, <a class="ref" href="analmetr.html#D11" target="_self" onmouseover="rs('analmetr/D11')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E21:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A13</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">p29</font>,<font color="Maroon" title="c25">q29</font>,<font color="Maroon" title="c21">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" target="_self" onmouseover="rs('analmetr/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<a NAME="E22:88"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:88"><span class="lab"><font color="Green" title="E61">A3</font></span></a>, <a class="txt" href="#E10:88"><span class="lab"><font color="Green" title="E67">A9</font></span></a>, <a class="ref" href="analmetr.html#D11" target="_self" onmouseover="rs('analmetr/D11')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E23:88"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">p29</font>,<font color="Maroon" title="c25">q29</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" target="_self" onmouseover="rs('analmetr/T40')" onmouseout="rh()">Th40</a></span>;<br/>
<a NAME="E24:88"/><span class="kw">then </span>
<font color="Maroon" title="c24">p29</font>,<font color="Maroon" title="c25">q29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c21">d9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:88"><span class="lab"><font color="Green" title="E71">A13</font></span></a>, <a class="ref" href="aff_1.html#T10" onmouseover="rs('aff_1/T10')" onmouseout="rh()">AFF_1:10</a></span>;<br/>
<a NAME="E25:88"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" target="_self" onmouseover="rs('analmetr/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:88"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:88"><span class="lab"><font color="Green" title="E65">A7</font></span></a>, <a class="txt" href="#E19:88"><span class="lab"><font color="Green" title="E70">A12</font></span></a>, <a class="ref" href="analmetr.html#D8" target="_self" onmouseover="rs('analmetr/D8')" onmouseout="rh()">Def7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
