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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="parsp_2.html#NM1">FanodesSp</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>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>











<b>assume </b><a NAME="E1:69"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:69_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:69_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="parsp_2.html#E1:69"><i><font color="Green">E56</font></i></a>, <a class="ref" href="parsp_2.html#T55" target="_self">Th55</a></i>;<br/><b>hence </b><a NAME="E3:69_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:69_2"/><i><font color="Green">E59</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>3</sub></font> &amp; <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="parsp_2.html#R1" target="_self">is_collinear</a>  )
 ;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:69_2"/><i><font color="Green">E60</font></i>: 
 <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="parsp_2.html#T51" target="_self">Th51</a></i>;<br/><a NAME="E4:69_2"/>
 <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="parsp_2.html#E3:69_2"><i><font color="Green">E60</font></i></a>, <a class="ref" href="parsp_2.html#T41" target="_self">Th41</a></i>;<br/><a NAME="E5:69_2"/><b>then </b>
(  <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="parsp_2.html#E1:69"><i><font color="Green">E56</font></i></a>, <a class="txt" href="parsp_2.html#E1:69_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="parsp_2.html#T62" target="_self">Th62</a></i>;<br/><b>hence </b><a NAME="E6:69_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="parsp_2.html#T43" target="_self">Th43</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:69_3"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; not <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="parsp_2.html#R1" target="_self">is_collinear</a>  )
 ;<br/><a NAME="E2:69_3"/><b>then </b>
(  <a href="parsp_2.html#R2" target="_self">parallelogram</a> <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> &amp;  <a href="parsp_2.html#R2" target="_self">parallelogram</a> <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>6</sub></font> )
 <b>by </b><i><a class="txt" href="parsp_2.html#E1:69"><i><font color="Green">E56</font></i></a>, <a class="ref" href="parsp_2.html#T60" target="_self">Th60</a></i>;<br/><b>hence </b><a NAME="E3:69_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="parsp_2.html#T43" target="_self">Th43</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:69"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="parsp_2.html#E2:69"><i><font color="Green">E57</font></i></a>, <a class="txt" href="parsp_2.html#E3:69"><i><font color="Green">E58</font></i></a></i>;<br/>


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