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<b>let </b><font color="Maroon" title="c1">SAS</font> be   <a href="semi_af1.html#NM1" title="SEMI_AF1:NM.1">Semi_Affine_Space</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>;<br/>





<b>assume </b><a NAME="E1:55"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">d</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font><b> such that </b><br/><a NAME="E3:55"/><i><font color="Green" title="E45">A1</font></i>: 
not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c4">b</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="semi_af1.html#T41" target="_self" title="SEMI_AF1:th.41">Th41</a></i>;<br/>
<a NAME="E4:55"/>
not <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">d</font> <a href="semi_af1.html#R1" title="SEMI_AF1:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="semi_af1.html#E3:55"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="semi_af1.html#T37" target="_self" title="SEMI_AF1:th.37">Th37</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font><b> such that </b><br/><a NAME="E6:55"/><i><font color="Green" title="E46">A2</font></i>: 
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">d</font>,<font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="semi_af1.html#T62" target="_self" title="SEMI_AF1:th.62">Th62</a></i>;<br/>
<a NAME="E7:55"/>
 <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">d</font>
 
<b>by </b><i><a class="txt" href="semi_af1.html#E6:55"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="semi_af1.html#T61" target="_self" title="SEMI_AF1:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E8:55"/>
 ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font> st  <a href="semi_af1.html#R2" title="SEMI_AF1:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font>,<font color="Maroon" title="c3">d</font>
 ;<br/>


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