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<b>let </b><font color="Maroon" title="c1">CPS</font> be  <a href="collsp.html#V4" title="COLLSP:attr.4">proper</a> <a href="collsp.html#NM2" title="COLLSP:NM.2">CollSp</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">P</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">p'</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">CPS</font>;<br/><b>let </b><font color="Maroon" title="c5">P'</font> be    <a href="incproj.html#M1" title="INCPROJ:mode.1">LINE</a> of <font color="Maroon" title="c1">CPS</font>;<br/>









<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E4">A1</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p'</font> &amp; <font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P'</font> )
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:8_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="c3">P</font>
 ;<br/><a NAME="E2:8_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c5">P'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="incproj.html#K2" title="INCPROJ:func.2">Proj_Inc</a> <font color="Maroon" title="c1">CPS</font>
 <b>by </b><i><a class="txt" href="incproj.html#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="incsp_1.html#D1" title="INCSP_1:def.1">INCSP_1:def 1</a></i>;<br/><a NAME="E3:8_1"/><b>then </b>
 ex <font color="Olive" title="b1">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c5">P'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Maroon" title="c4">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D2" target="_self" title="INCPROJ:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E4:8_1"/>
<font color="Maroon" title="c4">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P'</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:8"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c4">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P'</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">P''</font> = <font color="Maroon" title="c5">P'</font> as   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" title="INCPROJ:func.3">IncProjSp_of</a> <font color="Maroon" title="c1">CPS</font></span>)</span> <b>by </b><i><a class="ref" href="incproj.html#T2" target="_self" title="INCPROJ:th.2">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">P'''</font> = <font color="Maroon" title="c6">P''</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="incproj.html#K1" title="INCPROJ:func.1">ProjectiveLines</a> <font color="Maroon" title="c1">CPS</font> ;<br/>
<a NAME="E6:8"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c7">P'''</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="incproj.html#K2" title="INCPROJ:func.2">Proj_Inc</a> <font color="Maroon" title="c1">CPS</font>
 
<b>by </b><i><a class="txt" href="incproj.html#E3:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="incproj.html#D2" target="_self" title="INCPROJ:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon" title="c2">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="txt" href="incproj.html#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="incsp_1.html#D1" title="INCSP_1:def.1">INCSP_1:def 1</a></i>;<br/>


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