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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">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<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>assume </b><a NAME="E1:41"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:41"/><b>then </b><i><font color="Green">E35</font></i>: 
( <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> &amp; <font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:41"><i><font color="Green">E35</font></i></a>, </i>;<br/>
<a NAME="E4:41"/><b>then </b>
<font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<a NAME="E5:41"/><b>then </b>
<font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="aff_1.html#T58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E6:41"/>
<font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T59">AFF_1:59</a></i>;<br/>


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