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<b>let </b><font color="Maroon" title="c1">G</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">b</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c5">A</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>;<br/>









<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c1">G</font> is <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a2</font> &amp; <font color="Maroon" title="c4">b</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">b</font> <a href="projpl_1.html#R4" title="PROJPL_1:pred.4">is_collinear</a>  )
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green" title="E17">A2</font></i>: 
( <font color="Maroon" title="c2">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">A</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">A</font> )
 
<b>by </b><i><a class="ref" href="incproj.html#D7" title="INCPROJ:def.7">INCPROJ:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">P</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:18"/><i><font color="Green" title="E18">A3</font></i>: 
( <font color="Maroon" title="c2">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c4">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">P</font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="projpl_1.html#T5" target="_self" title="PROJPL_1:th.5">Th5</a></i>;<br/>
<b>thus </b><a NAME="E5:18"/>
contradiction
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="projpl_1.html#E2:18"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="projpl_1.html#E4:18"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></i>;<br/>


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