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<b>let </b><font color="Maroon" title="c1">IPP</font> be   <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</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> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>  ex <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font>, <font color="Olive" title="b4">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 <br/>( <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">C</font> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">C</font> &amp; <font color="Olive" title="b4">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">A</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <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 <br/>( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <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="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b3">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> )</span><br/>



<b>consider </b><font color="Maroon" title="c3">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E2:5"/><i><font color="Green" title="E4">A1</font></i>: 
not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">Q</font>
 <b>by </b><i><a class="ref" href="projred1.html#T2" target="_self" title="PROJRED1:th.2">Th2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">b3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E4:5"/><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c4">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b3</font> &amp; <font color="Maroon" title="c6">b3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b1</font> &amp; <font color="Maroon" title="c4">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">Q</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">Q</font> &amp; <font color="Maroon" title="c6">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">Q</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D12" title="INCPROJ:def.12">INCPROJ:def 12</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">B1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E6:5"/><i><font color="Green" title="E6">A3</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B1</font> &amp; <font color="Maroon" title="c4">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B1</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">B2</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E8:5"/><i><font color="Green" title="E7">A4</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">B2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">B2</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">B3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U2" title="INCSP_1:sel.2">Lines</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E10:5"/><i><font color="Green" title="E8">A5</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">B3</font> &amp; <font color="Maroon" title="c6">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">B3</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/>
<a NAME="E11:5"/><i><font color="Green" title="E9">A6</font></i>: 
not <font color="Maroon" title="c4">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">B2</font>
 
<b>by </b><i><a class="txt" href="#E2:5"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E4:5"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="#E8:5"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E12:5"/><i><font color="Green" title="E10">A7</font></i>: 
not <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">B3</font>
 
<b>by </b><i><a class="txt" href="#E2:5"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E4:5"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="#E10:5"><i><font color="Green" title="E8">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E13:5"/>
not <font color="Maroon" title="c6">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B1</font>
 
<b>by </b><i><a class="txt" href="#E2:5"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="#E4:5"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="#E6:5"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E14:5"/>
 ex <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 <br/>( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <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="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b3">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> )
 <b>by </b><i><a class="txt" href="#E6:5"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="#E8:5"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="#E10:5"><i><font color="Green" title="E8">A5</font></i></a>, <a class="txt" href="#E11:5"><i><font color="Green" title="E9">A6</font></i></a>, <a class="txt" href="#E12:5"><i><font color="Green" title="E10">A7</font></i></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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