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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/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_1"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>
 ;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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="c4">P</font>, <font color="Maroon" title="c5">Q</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><a NAME="E2:7_1"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c5">Q</font> )
 ;<br/><a NAME="E3:7_1"/><b>then </b>
( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">Q</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">Q</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D7" title="INCPROJ:def.7">INCPROJ:def 7</a></i>;<br/><b>hence </b><a NAME="E4:7_1"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> or <font color="Maroon" title="c4">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:7_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:7_2"/><i><font color="Green" title="E7">A2</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b3">P</font>, <font color="Olive" title="b4">Q</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Olive" title="b3">P</font> &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Olive" title="b4">Q</font> &amp; not <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> holds <br/><font color="Olive" title="b3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">Q</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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="c4">P</font>, <font color="Maroon" title="c5">Q</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><a NAME="E1:7_2_1"/>
( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">Q</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">Q</font> )
 ;<br/><a NAME="E2:7_2_1"/><b>then </b>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="incproj.html#R3" title="INCPROJ:pred.3">on</a> <font color="Maroon" title="c5">Q</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D7" title="INCPROJ:def.7">INCPROJ:def 7</a></i>;<br/><b>hence </b><a NAME="E3:7_2_1"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> or <font color="Maroon" title="c4">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:7_2"><i><font color="Green" title="E7">A2</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:7_2"/>
<font color="Maroon" title="c1">G</font> is <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>
 <b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></i>;<br/></div>
<b>end;</b></div>


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