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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="projpl_1.html#NM1" title="PROJPL_1:NM.1">IncProjectivePlane</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>, <font color="Olive" title="b4">d</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font>  holds <br/>(  not <font color="Olive" title="b1">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b4">d</font> or <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> or <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> or <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> or <font color="Olive" title="b1">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b4">d</font> )</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>, <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> or <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> or <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> or <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font> )</span><br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green" title="E33">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> &amp; not <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</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="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font></span><br/>

<a NAME="E2:38"/><b>then </b>
( <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="ref" href="projpl_1.html#T16" target="_self" title="PROJPL_1:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E3:38"/>
<font color="Maroon" title="c2">a</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c5">d</font>
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:38"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</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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