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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">a</font>, <font color="Maroon" title="c3">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="c4">A</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="E1:47"/><i><font color="Green" title="E42">A1</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a> 
 
<b>by </b><i><a class="ref" href="aff_1.html#T40" target="_self" title="AFF_1:th.40">Th40</a></i>;<br/>
<a NAME="E3:47"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="txt" href="aff_1.html#E1:47"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="aff_1.html#T48" target="_self" title="AFF_1:th.48">Th48</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
contradiction
 <b>by </b><i><a class="txt" href="aff_1.html#E1:47"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="aff_1.html#E2:47"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="aff_1.html#T37" target="_self" title="AFF_1:th.37">Th37</a></i>;<br/>


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