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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>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:29"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="incproj.html#R3">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="incproj.html#R3">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incproj.html#R3">on</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E3:29"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green">E26</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:29"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E2:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E5:29"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green">E26</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E6:29"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E7:29"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E2:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E8:29"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:29"><i><font color="Green">E26</font></i></a>, <a class="ref" href="projpl_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E9:29"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i><a class="ref" href="projpl_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E10:29"/><b>then </b>
<font color="Maroon">c<sub>8</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#E2:29"><i><font color="Green">E27</font></i></a>, <a class="ref" href="projpl_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E11:29"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="incproj.html#R1">are_mutually_different</a> 
 <b>by </b><i><a class="txt" href="projpl_1.html#E4:29"><i><font color="Green">E28</font></i></a>, <a class="txt" href="projpl_1.html#E7:29"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a></i>;<br/>


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