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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="E1:15"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E2:15"/><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">b</font>
 ;<br/>

<div><i><font color="Green">E31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font>
 ;<br/><div><i><font color="Green">E33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1"/>
<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>
 ;<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="E3:15_1_1"/><i><font color="Green">E34</font></i>: 
( <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> &amp; <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>and </b><br/><a NAME="E4:15_1_1"/>
<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E5:15_1_1"/>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">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="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/><b>hence </b><a NAME="E6:15_1_1"/>
 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="diraf.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> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_2"/>
<font color="Maroon">p</font>,<font color="Maroon">b</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">c</font>,<font color="Maroon">p</font>
 ;<br/><a NAME="E2:15_1_2"/><b>then </b>
<font color="Maroon">b</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="E4:15_1_2"/><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">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="Maroon">d</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <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="E5:15_1_2"/>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">d</font>,<font color="Maroon">p</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="Maroon">d</font> )
 <b>by </b><i>, <a class="ref" href="diraf.html#T5">DIRAF:5</a></i>;<br/><a NAME="E6:15_1_2"/><b>then </b>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">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="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/><b>hence </b><a NAME="E7:15_1_2"/>
 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="diraf.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> )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:15_1"/>
 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="diraf.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> )
 <b>by </b><i>, , <a class="ref" href="diraf.html#D4">DIRAF:def 4</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><a NAME="E2:15_2"/>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">p</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="diraf.html#R2">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">p</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T25">DIRAF:25</a></i>;<br/><b>hence </b><a NAME="E3:15_2"/>
 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="diraf.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> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:15"/>
 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="diraf.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> )
 <b>by </b><i/>;<br/>


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