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





<b>assume </b><a NAME="E1:53"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font><b> such that </b><br/><a NAME="E3:53"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a> 
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font><b> such that </b><br/><a NAME="E5:53"/><i><font color="Green">E18</font></i>: 
 <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i><a class="txt" href="parsp_2.html#E4"><i><font color="Green">Lemma44</font></i></a>, </i>;<br/>
<a NAME="E6:53"/>
not <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="parsp_2.html#E8:53"><i><font color="Green">E45</font></i></a>, </i>;<br/>
<b>then consider </b><font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font><b> such that </b><br/><a NAME="E8:53"/><i><font color="Green">E45</font></i>: 
 <a href="parsp_2.html#R2" target="_self">parallelogram</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/>
<a NAME="E9:53"/>
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="txt" href="parsp_2.html#E8:53"><i><font color="Green">E45</font></i></a>, , , </i>;<br/>
<a NAME="E10:53"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; not <font color="Maroon">a</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">p</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="txt" href="parsp_2.html#E8:53"><i><font color="Green">E45</font></i></a>, , <a class="ref" href="parsp_1.html#T43">PARSP_1:43</a></i>;<br/>
<a NAME="E11:53"/><b>then </b>
( <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; not <font color="Maroon">a</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">p</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="parsp_1.html#T40">PARSP_1:40</a></i>;<br/>
<a NAME="E12:53"/><b>then </b>
( <font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E13:53"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a>  &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E14:53"/>
 ex <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font> st <br/>( <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Olive">c</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a>  &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> )
 ;<br/>


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