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





<b>assume </b><a NAME="E1:85"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">X</font> <a href="aff_4.html#NR1" target="_self">is_plane</a> 
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:85_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><a NAME="E2:85_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">X</font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">X</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:85_1"/>
<font color="Maroon">a</font> <a href="aff_4.html#K3" target="_self">+</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <b>by </b><i>, <a class="txt" href="aff_4.html#E25"><i><font color="Green">Lemma68</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:85"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff <font color="Maroon">a</font> <a href="aff_4.html#K3" target="_self">+</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 <b>by </b><i>, <a class="txt" href="aff_4.html#E25"><i><font color="Green">Lemma68</font></i></a></i>;<br/>


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