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







<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><a NAME="E2:70_1"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:70_1"/>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font> st <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Olive">d</font>
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <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>  )
 ;<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>, <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="E3:70_2"/><i><font color="Green">E46</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#E6:70_2"><i><font color="Green">E48</font></i></a></i>;<br/><a NAME="E4:70_2"/><i><font color="Green">E47</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">a</font>,<font color="Maroon">b</font> &amp; not <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">c</font> <a href="parsp_2.html#R1" target="_self">is_collinear</a>  )
 <b>by </b><i>, , , </i>;<br/><b>then consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font><b> such that </b><br/><a NAME="E6:70_2"/><i><font color="Green">E48</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">c</font>,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/><a NAME="E7:70_2"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E8:70_2"/>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font> st <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Olive">d</font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_3"/>
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; not <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>  )
 ;<br/><b>then consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font><b> such that </b><br/><a NAME="E3:70_3"/><i><font color="Green">E49</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">c</font>,<font color="Maroon">d</font>
 <b>by </b><i/>;<br/><a NAME="E4:70_3"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:70_3"/>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font> st <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Olive">d</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:70"/>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FdSp</font> st <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_2.html#R3" target="_self">congr</a> <font color="Maroon">c</font>,<font color="Olive">d</font>
 <b>by </b><i>, </i>;<br/>


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