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<b>let </b><font color="Maroon">CPS</font> be  <a href="collsp.html#V4">proper</a> <a href="collsp.html#NM2">CollSp</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>;<br/>





<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font>, <font color="Maroon">q'</font> = <font color="Maroon">q</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CPS</font> ;<br/>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1"/>
<font color="Maroon">p'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q'</font>
 ;<br/><b>then consider </b><font color="Maroon">P'</font> being    <a href="incproj.html#M1" target="_self">LINE</a> of <font color="Maroon">CPS</font><b> such that </b><br/><a NAME="E3:12_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">p'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P'</font> &amp; <font color="Maroon">q'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P'</font> )
 <b>by </b><i><a class="ref" href="collsp.html#T24">COLLSP:24</a></i>;<br/><b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P'</font> as   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> <b>by </b><i/>;<br/><a NAME="E5:12_1"/>
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">P</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:12_1"/>
 ex <font color="Olive">P</font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> st <br/>( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> )
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font>
 ;<br/><b>consider </b><font color="Maroon">r'</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CPS</font><b> such that </b><br/><a NAME="E3:12_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">p'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">r'</font>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">P'</font> being    <a href="incproj.html#M1" target="_self">LINE</a> of <font color="Maroon">CPS</font><b> such that </b><br/><a NAME="E5:12_2"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">p'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P'</font> &amp; <font color="Maroon">r'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P'</font> )
 <b>by </b><i>, <a class="ref" href="collsp.html#T24">COLLSP:24</a></i>;<br/><b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P'</font> as   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> <b>by </b><i/>;<br/><a NAME="E7:12_2"/>
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">P</font> )
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E8:12_2"/>
 ex <font color="Olive">P</font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> st <br/>( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:12"/>
 ex <font color="Olive">P</font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> st <br/>( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">P</font> )
 <b>by </b><i/>;<br/>


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