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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">p</font>, <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><br/> for <font color="Olive" title="b4">K</font>, <font color="Olive" title="b5">L</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">K</font> &amp; not <font color="Olive" title="b1">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">L</font> &amp; <font color="Olive" title="b2">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">K</font> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b4">K</font>,<font color="Olive" title="b1">p</font>,<font color="Olive" title="b5">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> holds <br/><font color="Olive" title="b3">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font>, <font color="Olive" title="b2">L</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">K</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">p</font>,<font color="Olive" title="b2">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> holds <br/><font color="Maroon" title="c4">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">K</font>, <font color="Maroon" title="c6">L</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"> ( not <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">K</font> &amp; not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c5">K</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> implies <font color="Maroon" title="c4">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font> )</span><br/>











<span class="kw">assume </span><a NAME="E1:26"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
( not <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">K</font> &amp; not <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c5">K</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</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="c4">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">X</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
( <font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">X</font> &amp; <font color="Maroon" title="c3">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<a NAME="E4:26"/>
 ex <font color="Olive" title="b1">z</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">z</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font> &amp; <font color="Olive" title="b1">z</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D14" title="INCPROJ:def.14">INCPROJ:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26"/>
<font color="Maroon" title="c4">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="projred1.html#D1" target="_self" title="PROJRED1: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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