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<b>let </b><font color="Maroon">M</font> be   <a href="midsp_1.html#NM1">MidSp</a>;<br/><b>let </b><font color="Maroon">u</font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">w</font> be    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font>;<br/>







<b>assume </b><a NAME="E1:58"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">u</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">w</font>
 ;<br/>

<b>consider </b><font color="Maroon">u'</font> being    <a href="midsp_1.html#M1" target="_self">Vector</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E3:58"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">u</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">u'</font> <a href="hidden.html#R1">=</a>  <a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T21" target="_self">Th21</a></i>;<br/>
<font color="Maroon">v</font> = 
<font color="Maroon">v</font> <a href="midsp_1.html#K10" target="_self">+</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">u'</font></span>)</span> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">v</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T25" target="_self">Th25</a>, <a class="ref" href="midsp_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u'</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">u</font></span>)</span> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">v</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<font color="Maroon">u'</font> <a href="midsp_1.html#K10" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#T24" target="_self">Th24</a>, <a class="ref" href="midsp_1.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">u'</font> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">u</font></span>)</span> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">w</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font></span>)</span> <a href="midsp_1.html#K10" target="_self">+</a> <font color="Maroon">w</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T25" target="_self">Th25</a>, <a class="ref" href="midsp_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<font color="Maroon">w</font> <a href="midsp_1.html#K10" target="_self">+</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K9" target="_self">ID</a> <font color="Maroon">M</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#T22" target="_self">Th22</a></i>
;<br/>
<b>hence </b><a NAME="E5:58"/>
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#D5" target="_self">Def5</a></i>;<br/>


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