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











<b>assume </b><a NAME="E1:8"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">A</font> <a href="aff_1.html#R4">//</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> )
 ;<br/>

<a NAME="E2:8"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a> 
 
<b>by </b><i><a class="ref" href="aff_1.html#T50">AFF_1:50</a></i>;<br/>
<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a'</font>
 ;<br/><b>consider </b><font color="Maroon">d'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font><b> such that </b><br/><a NAME="E3:8_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">a'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">d'</font>
 <b>and </b><br/><a NAME="E4:8_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">d'</font>
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E5:8_1"/>
<font color="Maroon">d</font>,<font color="Maroon">d'</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a</font>,<font color="Maroon">a'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T13">AFF_1:13</a></i>;<br/><a NAME="E6:8_1"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">d'</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , <a class="ref" href="aff_1.html#T41">AFF_1:41</a></i>;<br/><a NAME="E7:8_1"/><b>then </b>
<font color="Maroon">d</font>,<font color="Maroon">d'</font> <a href="aff_1.html#R2">//</a> <font color="Maroon">K</font>
 <b>by </b><i>, </i>;<br/><a NAME="E8:8_1"/><b>then </b>
<font color="Maroon">d'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E9:8_1"/>
 ex <font color="Olive">d'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Olive">d'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Olive">d'</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font>
 ;<br/><b>take </b><font color="Maroon">d'</font> = <font color="Maroon">d</font>;<br/><b>thus </b><a NAME="E2:8_2"/>
<font color="Maroon">d'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E3:8_2"/>
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Maroon">d'</font>
 <b>by </b><i>, <a class="ref" href="aff_1.html#T11">AFF_1:11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:8"/>
 ex <font color="Olive">d'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Olive">d'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">a'</font>,<font color="Olive">d'</font> )
 <b>by </b><i/>;<br/>


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