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<b>let </b><font color="Maroon" title="c1">G</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</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>, <font color="Maroon" title="c5">d</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c6">P</font>, <font color="Maroon" title="c7">Q</font>, <font color="Maroon" title="c8">R</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:29"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="projpl_1.html#R5" title="PROJPL_1:pred.5">is_a_quadrangle</a> 
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green" title="E27">A2</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c6">P</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c7">Q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c8">R</font> )
 ;<br/>

<a NAME="E3:29"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self" title="PROJPL_1:def.6">Def6</a></i>;<br/>
<a NAME="E4:29"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon" title="c6">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Q</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E2:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self" title="PROJPL_1:th.19">Th19</a></i>;<br/>
<a NAME="E5:29"/>
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self" title="PROJPL_1:def.6">Def6</a></i>;<br/>
<a NAME="E6:29"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></i>;<br/>
<a NAME="E7:29"/><b>then </b><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c7">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">R</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E2:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self" title="PROJPL_1:th.19">Th19</a></i>;<br/>
<a NAME="E8:29"/>
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self" title="PROJPL_1:def.6">Def6</a></i>;<br/>
<a NAME="E9:29"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> <a href="projpl_1.html#NR6" title="PROJPL_1:NR.6">is_a_triangle</a> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self" title="PROJPL_1:th.11">Th11</a></i>;<br/>
<a NAME="E10:29"/><b>then </b>
<font color="Maroon" title="c8">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">P</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E2:29"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self" title="PROJPL_1:th.19">Th19</a></i>;<br/>
<b>hence </b><a NAME="E11:29"/>
<font color="Maroon" title="c6">P</font>,<font color="Maroon" title="c7">Q</font>,<font color="Maroon" title="c8">R</font> <a href="incproj.html#R1" title="INCPROJ:pred.1">are_mutually_different</a> 
 <b>by </b><i><a class="txt" href="projpl_1.html#E4:29"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="projpl_1.html#E7:29"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="incproj.html#D5" title="INCPROJ:def.5">INCPROJ:def 5</a></i>;<br/>


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