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<b>let </b><font color="Maroon">OAS</font> be   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E3:14"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 ;<br/>

<b>consider </b><font color="Maroon">q</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font><b> such that </b><br/><a NAME="E5:14"/><i><font color="Green">E32</font></i>: 
 <a href="diraf.html#R1">Mid</a> <font color="Maroon">b</font>,<font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E6:14"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T17">DIRAF:17</a></i>;<br/>
<a NAME="E7:14"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">p</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="diraf.html#D3">DIRAF:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">r</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font><b> such that </b><br/><a NAME="E9:14"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E10:14"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E11:14"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E12:14"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 <b>by </b><i>, , </i>;<br/>
<a NAME="E13:14"/>
<font color="Maroon">b</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, <a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/>
<a NAME="E14:14"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, , <a class="ref" href="analoaf.html#D5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E15:14"/><b>then </b>
<font color="Maroon">q</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font><b> such that </b><br/><a NAME="E17:14"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">r</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">d</font>
 <b>and </b><br/><a NAME="E18:14"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">r</font>,<font color="Maroon">q</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 <b>and </b><br/><a NAME="E19:14"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 <b>and </b><br/><a NAME="E20:14"/>
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 <b>by </b><i>, , </i>;<br/>
<a NAME="E21:14"/>
<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="diraf.html#T27">DIRAF:27</a></i>;<br/>
<a NAME="E22:14"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Maroon">d</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T28">DIRAF:28</a></i>;<br/>
<a NAME="E23:14"/>
<font color="Maroon">p</font>,<font color="Maroon">r</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, <a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/>
<a NAME="E24:14"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, , <a class="ref" href="diraf.html#T6">DIRAF:6</a></i>;<br/>
<a NAME="E25:14"/><b>then </b>
<font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/>
<b>hence </b><a NAME="E26:14"/>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">OAS</font> st <br/>( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">p</font>,<font color="Olive">d</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">c</font>,<font color="Olive">d</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> )
 <b>by </b><i>, </i>;<br/>


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