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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="incsp_1.html#NM4" title="INCSP_1:NM.4">IncSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">L</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c2">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">L</font>
 ;<br/>

<b>given </b><font color="Maroon" title="c4">A</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><a NAME="E2:56"/><i><font color="Green" title="E39">A2</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font> &amp; <font color="Maroon" title="c4">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">B</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E4:56"/><i><font color="Green" title="E40">A3</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">B</font>
 <b>and </b><br/><a NAME="E5:56"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">K</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E50"><i><font color="Green" title="E26">Lm1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">C</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E7:56"/><i><font color="Green" title="E42">A5</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">C</font>
 <b>and </b><br/><a NAME="E8:56"/><i><font color="Green" title="E43">A6</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E50"><i><font color="Green" title="E26">Lm1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">P1</font> =  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>;<br/>
<b>set </b><font color="Maroon" title="c8">P2</font> =  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>;<br/>
<a NAME="E9:56"/>
( <font color="Maroon" title="c2">K</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c2">K</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> &amp; <font color="Maroon" title="c3">L</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:56"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="incsp_1.html#E2:56"><i><font color="Green" title="E39">A2</font></i></a>, <a class="ref" href="incsp_1.html#D12" target="_self" title="INCSP_1:def.12">Def12</a></i>;<br/>
<a NAME="E10:56"/><b>then </b>
( <font color="Maroon" title="c4">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c6">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">A</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> &amp; <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> &amp; <font color="Maroon" title="c6">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E2:56"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="incsp_1.html#E5:56"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="incsp_1.html#E8:56"><i><font color="Green" title="E43">A6</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></i>;<br/>
<a NAME="E11:56"/><b>then </b><i><font color="Green" title="E44">A7</font></i>: 
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T14" target="_self" title="INCSP_1:th.14">Th14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#NR6" title="INCSP_1:NR.6">is_collinear</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c9">L1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:56_1"/><i><font color="Green" title="E45">A8</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font>
 <b>by </b><i><a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a></i>;<br/><a NAME="E4:56_1"/>
( <font color="Maroon" title="c4">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L1</font> &amp; <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L1</font> &amp; <font color="Maroon" title="c6">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">L1</font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E3:56_1"><i><font color="Green" title="E45">A8</font></i></a>, <a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></i>;<br/><a NAME="E5:56_1"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c2">K</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c9">L1</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E2:56"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="incsp_1.html#E5:56"><i><font color="Green" title="E41">A4</font></i></a>, <a class="txt" href="incsp_1.html#E8:56"><i><font color="Green" title="E43">A6</font></i></a>, <a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></i>;<br/><a NAME="E6:56_1"/><b>then </b>
( <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">L1</font> &amp; <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">L1</font> )
 <b>by </b><i><a class="txt" href="incsp_1.html#E4:56"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="incsp_1.html#E7:56"><i><font color="Green" title="E42">A5</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></i>;<br/><b>hence </b><a NAME="E7:56_1"/>
contradiction
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:56"><i><font color="Green" title="E38">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:56"/>
 <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K4" title="INCSP_1:func.4">Plane</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">K</font>
 <b>by </b><i><a class="txt" href="incsp_1.html#E11:56"><i><font color="Green" title="E44">A7</font></i></a>, <a class="ref" href="incsp_1.html#D8" target="_self" title="INCSP_1:def.8">Def8</a></i>;<br/>


</div>
