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<b>let </b><font color="Maroon">AS</font> be   <a href="diraf.html#NM1">AffinSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/>





<b>assume </b><a NAME="E1:48"/>
<font color="Maroon">A</font> <a href="aff_1.html#R3" target="_self">//</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E2:48"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="aff_1.html#K2" target="_self">Line</a> <font color="Olive">a</font>,<font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="aff_1.html#R2" target="_self">//</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="txt" href="aff_1.html#E15"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:48"/>
( <font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">C</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  )
 <b>by </b><i>, <a class="txt" href="aff_1.html#E19"><i><font color="Green">Lemma35</font></i></a></i>;<br/>


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