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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#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/>











<b>assume </b><a NAME="E1:13"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">t</font> &amp;  <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font> )
 ;<br/>

<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E2:13_1"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:13_1"/><b>then </b>
<font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">u</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:13_1"/>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E2:13_2"/>
( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">z</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E3:13_2"/><b>then </b>
( <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, </i>;<br/><a NAME="E4:13_2"/><b>then </b>
( <font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">u</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>;<br/><a NAME="E5:13_2"/><b>then </b>
<font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">u</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:13_2"/>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:13"/>
 <a href="aff_1.html#R1" target="_self">LIN</a> <font color="Maroon">z</font>,<font color="Maroon">t</font>,<font color="Maroon">u</font>
 <b>by </b><i/>;<br/>


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