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<b>let </b><font color="Maroon">G</font> be    <a href="incsp_1.html#L1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/>









<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:20"/><b>then </b><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E4:20"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:20"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:20"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  &amp; <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:20"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , </i>;<br/>

<b>thus </b><a NAME="E8:20"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E9:20"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E10:20"/>
<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E11:20"/>
<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E12:20"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E13:20"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E14:20"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E15:20"/>
<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E16:20"/>
<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E17:20"/>
<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E18:20"/>
<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E19:20"/>
<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E20:20"/>
<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E21:20"/>
<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E22:20"/>
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E23:20"/>
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E24:20"/>
<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E25:20"/>
<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E26:20"/>
<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E27:20"/>
<font color="Maroon">d</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E28:20"/>
<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>

<b>thus </b><a NAME="E29:20"/>
<font color="Maroon">d</font>,<font color="Maroon">c</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>by </b><i>, , , , </i>;<br/>


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