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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">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>;<br/>







<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E49">A1</font></i>: 
not <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">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/>

<a NAME="E2:62"/><b>then </b>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T36" target="_self" title="INCSP_1:th.36">Th36</a></i>;<br/>
<a NAME="E3:62"/><b>then </b><i><font color="Green" title="E50">A2</font></i>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">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>  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>
 
<b>by </b><i><a class="ref" href="incsp_1.html#D19" target="_self" title="INCSP_1:def.19">Def19</a></i>;<br/>
<a NAME="E4:62"/><b>then </b>
( <font color="Maroon" title="c2">A</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a>  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c3">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a>  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T11" target="_self" title="INCSP_1:th.11">Th11</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
( <font color="Maroon" title="c4">C</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a>  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> implies <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">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>  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E6:62"/><b>then </b>
( <font color="Maroon" title="c4">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span> &amp;  <a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="incsp_1.html#R3" title="INCSP_1:pred.3">on</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E1:62"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a>, <a class="ref" href="incsp_1.html#D21" target="_self" title="INCSP_1:def.21">Def21</a></i>;<br/>
<a NAME="E7:62"/><b>then </b>
( <font color="Maroon" title="c4">C</font> <a href="incsp_1.html#R2" title="INCSP_1:pred.2">on</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="incsp_1.html#E3:62"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="incsp_1.html#T35" target="_self" title="INCSP_1:th.35">Th35</a></i>;<br/>
<a NAME="E8:62"/><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="c2">A</font>,<font color="Maroon" title="c3">B</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">C</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="incsp_1.html#R5" title="INCSP_1:pred.5">on</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="incsp_1.html#T19" target="_self" title="INCSP_1:th.19">Th19</a></i>;<br/>
<a NAME="E9:62"/><b>then </b>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">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#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>;<br/>
<b>hence </b><a NAME="E10:62"/>
 <a href="incsp_1.html#K2" title="INCSP_1:func.2">Plane</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="incsp_1.html#K3" title="INCSP_1:func.3">Plane</a> <font color="Maroon" title="c4">C</font>,<span class="p1">(<span class="default"><a href="incsp_1.html#K1" title="INCSP_1:func.1">Line</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="incsp_1.html#E1:62"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="incsp_1.html#D20" target="_self" title="INCSP_1:def.20">Def20</a></i>;<br/>


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