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<b>let </b><font color="Maroon">AS</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="analoaf.html#L1">AffinStruct</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="analoaf.html#NM2">OAffinPlane</a>;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">AS</font> <a href="hidden.html#R1">=</a>  <a href="diraf.html#K2" target="_self">Lambda</a> <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">AS</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>, <font color="Maroon">t</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>;<br/>

<b>assume </b><a NAME="E2:55"/><i><font color="Green">E26</font></i>: 
not <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Maroon">t</font>
 ;<br/>

<a NAME="E3:55"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">AS</font> <a href="hidden.html#R1">=</a>  <a href="analoaf.html#G1">AffinStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="diraf.html#K1" target="_self">lambda</a> the <a href="analoaf.html#U1">CONGR</a> of <font color="Maroon">S</font></span>)</span> #)
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font>, <font color="Maroon">z'</font> = <font color="Maroon">z</font>, <font color="Maroon">t'</font> = <font color="Maroon">t</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E5:55"/>
not <font color="Maroon">x'</font>,<font color="Maroon">y'</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z'</font>,<font color="Maroon">t'</font>
 
<b>by </b><i>, , </i>;<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="E7:55"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x'</font>,<font color="Maroon">y'</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">x'</font>,<font color="Maroon">u'</font> &amp; <font color="Maroon">z'</font>,<font color="Maroon">t'</font> <a href="diraf.html#R2" target="_self">'||'</a> <font color="Maroon">z'</font>,<font color="Maroon">u'</font> )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">u'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> <b>by </b><i/>;<br/>
<a NAME="E9:55"/>
( <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> &amp; <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="E10:55"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">x</font>,<font color="Olive">u</font> &amp; <font color="Maroon">z</font>,<font color="Maroon">t</font> <a href="analoaf.html#R2">//</a> <font color="Maroon">z</font>,<font color="Olive">u</font> )
 ;<br/>


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