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<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</a>;<br/><b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">w</font> be    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font>;<br/>







<b>assume </b><a NAME="E1:58"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c4">w</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">u'</font> being    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E3:58"/><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c5">u'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T65" target="_self" title="MIDSP_1:th.65">Th65</a></i>;<br/>
<font color="Maroon" title="c3">v</font> = 
<font color="Maroon" title="c3">v</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#T64" target="_self" title="MIDSP_1:th.64">Th64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c5">u'</font></span>)</span> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="midsp_1.html#E3:58"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="midsp_1.html#T66" target="_self" title="MIDSP_1:th.66">Th66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">u'</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T66" target="_self" title="MIDSP_1:th.66">Th66</a></i>
<br/>.= 
<font color="Maroon" title="c5">u'</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="txt" href="midsp_1.html#E1:58"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="midsp_1.html#T63" target="_self" title="MIDSP_1:th.63">Th63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">u'</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c4">w</font>
<b>by </b><i><a class="ref" href="midsp_1.html#T63" target="_self" title="MIDSP_1:th.63">Th63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font></span>)</span> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <font color="Maroon" title="c4">w</font>
<b>by </b><i><a class="txt" href="midsp_1.html#E3:58"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="midsp_1.html#T66" target="_self" title="MIDSP_1:th.66">Th66</a></i>
<br/>.= 
<font color="Maroon" title="c4">w</font> <a href="midsp_1.html#K10" title="MIDSP_1:func.10">+</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K9" title="MIDSP_1:func.9">ID</a> <font color="Maroon" title="c1">M</font></span>)</span>
<b>by </b><i><a class="ref" href="midsp_1.html#T66" target="_self" title="MIDSP_1:th.66">Th66</a></i>
;<br/>
<b>hence </b><a NAME="E5:58"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">w</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T64" target="_self" title="MIDSP_1:th.64">Th64</a></i>;<br/>


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