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<b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c2">o</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>;<br/>







<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E6">A1</font></i>: 
( not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> &amp; not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">B</font> )
 ;<br/>

<div><i><font color="Green" title="E7">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:7_1"/><i><font color="Green" title="E8">A3</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c5">x</font> as   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> ;<br/><a NAME="E3:7_1"/>
<font color="Maroon" title="c6">x'</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="projred2.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="projred2.html#E1:7_1"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:7_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:7_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 ;<br/><a NAME="E2:7_2"/><b>then </b>
 ex <font color="Olive" title="b1">b</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">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Olive" title="b1">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><b>hence </b><a NAME="E3:7_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 <b>by </b><i><a class="txt" href="projred2.html#E1:7"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:7"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="projred2.html#E2:7"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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