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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b3">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="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> holds <br/><span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">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> </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> &amp; <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#NR6" title="INCSP_1:NR.6">is_collinear</a>  )</span><br/>







<b>assume </b><a NAME="E1:60"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <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> or <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>  )</span><br/>

<a NAME="E2:60"/><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="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="E3:60"/><b>then </b><i><font color="Green" title="E49">A1</font></i>: 
( <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/>
<b>assume </b><a NAME="E4:60"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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> </span><br/>

<a NAME="E5:60"/><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#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="txt" href="incsp_1.html#E3:60"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="incsp_1.html#T12" target="_self" title="INCSP_1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E6:60"/>
<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> 
 <b>by </b><i><a class="ref" href="incsp_1.html#D6" target="_self" title="INCSP_1:def.6">Def6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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