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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="incsp_1.html#L1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is   <a href="incproj.html#NM2">IncProjSp</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:17"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="incproj.html#R3">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="incproj.html#R1">are_mutually_different</a>  )
 <b>by </b><i><a class="ref" href="projpl_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E4:17"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="projpl_1.html#E3:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a></i>;<br/>
<a NAME="E5:17"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="projpl_1.html#E3:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D7">INCPROJ:def 7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> )
 </span><b>by </b><i><a class="txt" href="projpl_1.html#E1:17"><i><font color="Green">E15</font></i></a>, <a class="txt" href="projpl_1.html#E4:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projpl_1.html#E5:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_1"><b>case </b></a><a NAME="E1:17_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:17_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E4:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projpl_1.html#E5:17"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_2"><b>case </b></a><a NAME="E1:17_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:17_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E4:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projpl_1.html#E5:17"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:17"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>


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