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

<span class="kw">let </span><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>  st  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">a9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">b9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b6">x</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">x</font> holds <br/><font color="Olive" title="b5">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">a9</font>, <font color="Maroon" title="c6">b9</font>, <font color="Maroon" title="c7">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">a9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">b9</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">x</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c7">x</font> implies <font color="Maroon" title="c6">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">a9</font>
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">and </span><br/><a NAME="E4:67"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c7">x</font>
 <span class="kw">and </span><br/><a NAME="E5:67"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>
 <span class="kw">and </span><br/><a NAME="E6:67"/><span class="lab"><font color="Green" title="E58">A6</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c7">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">A</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">C</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">P</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>);<br/>
<a NAME="E7:67"/><span class="lab"><font color="Green" title="E59">A7</font></span>: 
<font color="Maroon" title="c5">a9</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="c5">a9</font>,<font color="Maroon" title="c6">b9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:67"/><span class="lab"><font color="Green" title="E60">A8</font></span>: 
<font color="Maroon" title="c6">b9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E9:67"/><span class="lab"><font color="Green" title="E61">A9</font></span>: 
<font color="Maroon" title="c5">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:67_1"/><span class="lab"><font color="Green" title="E62">A10</font></span>: 
<font color="Maroon" title="c5">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:67_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="aff_1.html#T54" target="_self" title="AFF_1:th.54">Th68</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:67_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E1:67_1"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="ref" href="aff_1.html#T55" target="_self" title="AFF_1:th.55">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A11</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" target="_self" title="AFF_1:def.3">Def3</a></span>;<br/>
<a NAME="E11:67"/><span class="lab"><font color="Green" title="E63">A12</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T7" target="_self" title="AFF_1:th.7">Th16</a></span>;<br/>
<a NAME="E12:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A13</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" target="_self" title="AFF_1:def.3">Def3</a></span>;<br/>
<a NAME="E13:67"/><span class="lab"><font color="Green" title="E65">A14</font></span>: 
<font color="Maroon" title="c6">b9</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="c5">a9</font>,<font color="Maroon" title="c6">b9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<a NAME="E14:67"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T7" target="_self" title="AFF_1:th.7">Th16</a></span>;<br/>
<a NAME="E15:67"/><span class="kw">then </span>
<font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c7">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="ref" href="aff_1.html#T5" target="_self" title="AFF_1:th.5">Th14</a></span>;<br/>
<a NAME="E16:67"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a9</font>,<font color="Maroon" title="c6">b9</font>,<font color="Maroon" title="c7">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" target="_self" title="AFF_1:def.1">Def1</a></span>;<br/>
<a NAME="E17:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A15</font></span>: 
<font color="Maroon" title="c7">x</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="c5">a9</font>,<font color="Maroon" title="c6">b9</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="ref" href="aff_1.html#T25" target="_self" title="AFF_1:th.25">Th39</a></span>;<br/>
<a NAME="E18:67"/><span class="lab"><font color="Green" title="E67">A16</font></span>: 
<font color="Maroon" title="c4">b</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="c2">o</font>,<font color="Maroon" title="c4">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<a NAME="E19:67"/><span class="lab"><font color="Green" title="E68">A17</font></span>: 
<font color="Maroon" title="c2">o</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="c2">o</font>,<font color="Maroon" title="c4">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<a NAME="E20:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A18</font></span>: 
<font color="Maroon" title="c7">x</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="c2">o</font>,<font color="Maroon" title="c4">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="ref" href="aff_1.html#T25" target="_self" title="AFF_1:th.25">Th39</a></span>;<br/>
<a NAME="E21:67"/>
<font color="Maroon" title="c6">b9</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="c2">o</font>,<font color="Maroon" title="c4">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E19:67"><span class="lab"><font color="Green" title="E68">A17</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="ref" href="aff_1.html#T25" target="_self" title="AFF_1:th.25">Th39</a></span>;<br/>
<a NAME="E22:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A19</font></span>: 
<font color="Maroon" title="c5">a9</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="c2">o</font>,<font color="Maroon" title="c4">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E7:67"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E69">A18</font></span></a>, <a class="txt" href="#E17:67"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="aff_1.html#T18" target="_self" title="AFF_1:th.18">Th30</a></span>;<br/>
<a NAME="E23:67"/><span class="lab"><font color="Green" title="E71">A20</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T7" target="_self" title="AFF_1:th.7">Th16</a></span>;<br/>
<a NAME="E24:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A21</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" target="_self" title="AFF_1:def.3">Def3</a></span>;<br/>
<a NAME="E25:67"/><span class="lab"><font color="Green" title="E73">A22</font></span>: 
<font color="Maroon" title="c5">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:67_2"/><span class="lab"><font color="Green" title="E74">A23</font></span>: 
<font color="Maroon" title="c5">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:67_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="aff_1.html#T55" target="_self" title="AFF_1:th.55">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:67_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E1:67_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="ref" href="aff_1.html#T55" target="_self" title="AFF_1:th.55">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E26:67"/><span class="lab"><font color="Green" title="E74">A24</font></span>: 
<font color="Maroon" title="c2">o</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="c2">o</font>,<font color="Maroon" title="c3">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<a NAME="E27:67"/><span class="lab"><font color="Green" title="E75">A25</font></span>: 
<font color="Maroon" title="c3">a</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="c2">o</font>,<font color="Maroon" title="c3">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th26</a></span>;<br/>
<a NAME="E28:67"/><span class="kw">then </span>
<font color="Maroon" title="c5">a9</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="c2">o</font>,<font color="Maroon" title="c3">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E23:67"><span class="lab"><font color="Green" title="E71">A20</font></span></a>, <a class="txt" href="#E24:67"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E26:67"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="ref" href="aff_1.html#T25" target="_self" title="AFF_1:th.25">Th39</a></span>;<br/>
<a NAME="E29:67"/><span class="kw">then </span>
<font color="Maroon" title="c4">b</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="c2">o</font>,<font color="Maroon" title="c3">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:67"><span class="lab"><font color="Green" title="E73">A22</font></span></a>, <a class="txt" href="#E24:67"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E12:67"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E26:67"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E19:67"><span class="lab"><font color="Green" title="E68">A17</font></span></a>, <a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E70">A19</font></span></a>, <a class="ref" href="aff_1.html#T18" target="_self" title="AFF_1:th.18">Th30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E30:67"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E24:67"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E26:67"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E27:67"><span class="lab"><font color="Green" title="E75">A25</font></span></a>, <a class="ref" href="aff_1.html#T21" target="_self" title="AFF_1:th.21">Th33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
