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









<b>assume </b><a NAME="E1:34"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z</font> )
 ;<br/>

<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">t</font>
 ;<br/><b>then consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:34_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">u</font> )
 <b>by </b><i>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><a NAME="E4:34_1"/>
( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Maroon">u</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E2:34"><i><font color="Green">E26</font></i></a>, </i>;<br/><b>hence </b><a NAME="E5:34_1"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">x</font>
 ;<br/><b>consider </b><font color="Maroon">p</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:34_2"/><i><font color="Green">E30</font></i>: 
(  <a href="diraf.html#R1" target="_self">Mid</a> <font color="Maroon">z</font>,<font color="Maroon">x</font>,<font color="Maroon">p</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font> )
 <b>by </b><i/>;<br/><a NAME="E4:34_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">p</font>
 <b>by </b><i>, </i>;<br/><b>then consider </b><font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E6:34_2"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> )
 <b>by </b><i>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><a NAME="E7:34_2"/>
<font color="Maroon">x</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="diraf.html#E2:34"><i><font color="Green">E26</font></i></a>, , <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><a NAME="E8:34_2"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">t</font>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E10:34_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">q</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">q</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">r</font> )
 <b>by </b><i>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><div><i><font color="Green">E34</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:34_2_1"/><b>then </b>
( <font color="Maroon">x</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">x</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y</font>,<font color="Maroon">x</font> )
 <b>by </b><i>, <a class="txt" href="diraf.html#E1:34_2"><i><font color="Green">E29</font></i></a>, </i>;<br/><a NAME="E3:34_2_1"/><b>then </b>
<font color="Maroon">z</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><a NAME="E4:34_2_1"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">x</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">t</font>,<font color="Maroon">t</font> )
 <b>by </b><i>, <a class="txt" href="diraf.html#E2:34"><i><font color="Green">E26</font></i></a>, <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/><a NAME="E5:34_2_1"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Maroon">t</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:34_2_1"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 ;<br/></div><b>end;</b></div><div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_2"/>
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E2:34_2_2"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">x</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">z</font> )
 <b>by </b><i>, <a class="txt" href="diraf.html#E1:34_2"><i><font color="Green">E29</font></i></a>, </i>;<br/><a NAME="E3:34_2_2"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">z</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">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">t</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E2:34"><i><font color="Green">E26</font></i></a>, , , </i>;<br/><a NAME="E4:34_2_2"/><b>then </b>
( <font color="Maroon">y</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">y</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Maroon">x</font> )
 <b>by </b><i>, , </i>;<br/><a NAME="E5:34_2_2"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Maroon">x</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:34_2_2"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_3"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> )
 ;<br/><a NAME="E2:34_2_3"/>
( <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">y</font>,<font color="Maroon">z</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">r</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">x</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">r</font>,<font color="Maroon">x</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:34_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="diraf.html#E3:34_2"><i><font color="Green">E30</font></i></a>, </i>;<br/><a NAME="E3:34_2_3"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">r</font>,<font color="Maroon">t</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">r</font>,<font color="Maroon">x</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E1:34_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="diraf.html#E10:34_2"><i><font color="Green">E33</font></i></a>, </i>;<br/><a NAME="E4:34_2_3"/><b>then </b>
( <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Maroon">r</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:34_2_3"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E14:34_2"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 <b>by </b><i><a class="txt" href="diraf.html#E4:34_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="diraf.html#E6:34_2"><i><font color="Green">E32</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:34"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Maroon">y</font>,<font color="Maroon">x</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">t</font>,<font color="Olive">u</font> )
 <b>by </b><i>, , </i>;<br/>


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