<?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="Red">::  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="Red">::  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="E1:79"/><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="E2:79"/><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="E3:79"/><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="E4:79"/><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="E5:79"/><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="E6:79"/><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="Red">::  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="E7:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:79"/><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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E9:79"/><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="79_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:79_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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:79_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="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="aff_1.html#T68" target="_self" title="AFF_1:th.68">Th68</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:79_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E6:79"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E8:79"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E1:79_1"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="ref" href="aff_1.html#T69" target="_self" title="AFF_1:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:79"/><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="E11:79"/><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="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T16" target="_self" title="AFF_1:th.16">Th16</a></span>;<br/>
<a NAME="E12:79"/><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="E13:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<a NAME="E14:79"/>
<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="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T16" target="_self" title="AFF_1:th.16">Th16</a></span>;<br/>
<a NAME="E15:79"/><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="#E5:79"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E6:79"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="ref" href="aff_1.html#T14" target="_self" title="AFF_1:th.14">Th14</a></span>;<br/>
<a NAME="E16:79"/><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="E17:79"/><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="#E9:79"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="txt" href="#E10:79"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E7:79"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E13:79"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="ref" href="aff_1.html#T39" target="_self" title="AFF_1:th.39">Th39</a></span>;<br/>
<a NAME="E18:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<a NAME="E19:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<a NAME="E20:79"/><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="#E4:79"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E11:79"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="txt" href="#E12:79"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E18:79"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" target="_self" title="AFF_1:th.39">Th39</a></span>;<br/>
<a NAME="E21:79"/>
<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="#E3:79"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E11:79"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="txt" href="#E12:79"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E19:79"><span class="lab"><font color="Green" title="E68">A17</font></span></a>, <a class="txt" href="#E18:79"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" target="_self" title="AFF_1:th.39">Th39</a></span>;<br/>
<a NAME="E22:79"/><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="#E8:79"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E12:79"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E10:79"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E7:79"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E13:79"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E20:79"><span class="lab"><font color="Green" title="E69">A18</font></span></a>, <a class="txt" href="#E17:79"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="ref" href="aff_1.html#T30" target="_self" title="AFF_1:th.30">Th30</a></span>;<br/>
<a NAME="E23:79"/><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="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="aff_1.html#T16" target="_self" title="AFF_1:th.16">Th16</a></span>;<br/>
<a NAME="E24:79"/><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="E25:79"/><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="79_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:79_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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:79_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="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E5:79"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="aff_1.html#T69" target="_self" title="AFF_1:th.69">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:79_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E6:79"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E8:79"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="txt" href="#E1:79_2"><span class="lab"><font color="Green" title="E74">A23</font></span></a>, <a class="ref" href="aff_1.html#T69" target="_self" title="AFF_1:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E26:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<a NAME="E27:79"/><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#T26" target="_self" title="AFF_1:th.26">Th26</a></span>;<br/>
<a NAME="E28:79"/><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="#E2:79"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E23:79"><span class="lab"><font color="Green" title="E71">A20</font></span></a>, <a class="txt" href="#E24:79"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E26:79"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="ref" href="aff_1.html#T39" target="_self" title="AFF_1:th.39">Th39</a></span>;<br/>
<a NAME="E29:79"/><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="#E25:79"><span class="lab"><font color="Green" title="E73">A22</font></span></a>, <a class="txt" href="#E24:79"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E12:79"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E26:79"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E19:79"><span class="lab"><font color="Green" title="E68">A17</font></span></a>, <a class="txt" href="#E18:79"><span class="lab"><font color="Green" title="E67">A16</font></span></a>, <a class="txt" href="#E22:79"><span class="lab"><font color="Green" title="E70">A19</font></span></a>, <a class="ref" href="aff_1.html#T30" target="_self" title="AFF_1:th.30">Th30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E30:79"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E24:79"><span class="lab"><font color="Green" title="E72">A21</font></span></a>, <a class="txt" href="#E26:79"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E27:79"><span class="lab"><font color="Green" title="E75">A25</font></span></a>, <a class="ref" href="aff_1.html#T33" target="_self" title="AFF_1:th.33">Th33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
