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<span class="kw">let </span><font color="Maroon" title="c1">IPP</font> be   <a href="incproj.html#V5" title="INCPROJ:attr.5">2-dimensional</a>   <a href="incproj.html#V9" title="INCPROJ:attr.9">Desarguesian</a>  <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  holds <br/>( <font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b3">C</font>,<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b3">C</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b1">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  )</span><br/><span class="kw">let </span><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#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  implies ( <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:5"/>
<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  )</span><br/>

<a NAME="E2:5"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">o</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">C</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5"/>
( <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c2">A</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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