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







<b>assume </b><b>that </b><br/><a NAME="E1:77"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">X</font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E2:77"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">Y</font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">Z</font>
 <b>and </b><br/><a NAME="E3:77"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> <b>by </b><i><a class="ref" href="aff_4.html#T18" target="_self">Th18</a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>now </b></a><div class="add"><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#NM2">Subset</a> of <font color="Maroon">AS</font>;<br/><b>assume </b><a NAME="E1:77_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">A</font> <a href="aff_1.html#NR2" target="_self">is_line</a>  &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> )
 ;<br/><a NAME="E2:77_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">p</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="aff_4.html#T18" target="_self">Th18</a>, <a class="txt" href="aff_4.html#E1:77_1"><i><font color="Green">E37</font></i></a></i>;<br/><a NAME="E3:77_1"/>
<font color="Maroon">p</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>, </i>;<br/><a NAME="E4:77_1"/><b>then </b>
<font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <b>by </b><i>, , <a class="txt" href="aff_4.html#E24"><i><font color="Green">Lemma67</font></i></a>, <a class="txt" href="aff_4.html#E1:77_1"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E5:77_1"/>
<font color="Maroon">a</font> <a href="aff_4.html#K2" target="_self">*</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <b>by </b><i>, <a class="txt" href="aff_4.html#E1:77"><i><font color="Green">E34</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:77"/>
<font color="Maroon">X</font> <a href="aff_4.html#R1" target="_self">'||'</a> <font color="Maroon">Z</font>
 <b>by </b><i/>;<br/>


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