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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c5">K</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/>









<b>assume </b><a NAME="E1:59"/><i><font color="Green" title="E51">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">K</font> &amp; not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c5">K</font> )
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:59"/><i><font color="Green" title="E52">A2</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:59"/><i><font color="Green" title="E53">A3</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c6">A</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/>
<a NAME="E4:59"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E3:59"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="aff_1.html#T15" target="_self" title="AFF_1:th.15">Th15</a></i>;<br/>
<a NAME="E5:59"/><b>then </b><i><font color="Green" title="E54">A4</font></i>: 
<font color="Maroon" title="c2">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="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" target="_self" title="AFF_1:def.2">Def2</a></i>;<br/>
<a NAME="E6:59"/><i><font color="Green" title="E55">A5</font></i>: 
<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="c3">a</font>,<font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T26" target="_self" title="AFF_1:th.26">Th26</a></i>;<br/>
<a NAME="E7:59"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E1:59"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="aff_1.html#E2:59"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="aff_1.html#D5" target="_self" title="AFF_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E8:59"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_1.html#E1:59"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="aff_1.html#E5:59"><i><font color="Green" title="E54">A4</font></i></a>, <a class="txt" href="aff_1.html#E6:59"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="aff_1.html#T59" target="_self" title="AFF_1:th.59">Th59</a></i>;<br/>


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