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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> holds  <font color="Olive" title="b1">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Olive" title="b1">u</font></span><br/><b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font> be    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c2">u</font></span><br/>





<b>consider </b><font color="Maroon" title="c4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>;<br/>
<b>consider </b><font color="Maroon" title="c5">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E3:55"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T55" target="_self" title="MIDSP_1:th.55">Th55</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E5:55"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">c</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T55" target="_self" title="MIDSP_1:th.55">Th55</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E7:55"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c7">d</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T55" target="_self" title="MIDSP_1:th.55">Th55</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">c'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E9:55"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c7">d</font>,<font color="Maroon" title="c8">c'</font>
 <b>by </b><i><a class="ref" href="midsp_1.html#T55" target="_self" title="MIDSP_1:th.55">Th55</a></i>;<br/>
<i><font color="Green" title="E44">A5</font></i>: <font color="Maroon" title="c4">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c8">c'</font> = 
<font color="Maroon" title="c5">b</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c7">d</font>
<b>by </b><i><a class="txt" href="#E3:55"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="#E9:55"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="midsp_1.html#T44" target="_self" title="MIDSP_1:th.44">Th44</a></i>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="midsp_1.html#K3" title="MIDSP_1:func.3">@</a> <font color="Maroon" title="c6">c</font>
<b>by </b><i><a class="txt" href="#E5:55"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="#E7:55"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="midsp_1.html#T44" target="_self" title="MIDSP_1:th.44">Th44</a></i>
;<br/>
<font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c3">v</font> = 
 <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c6">c</font>
<b>by </b><i><a class="txt" href="#E3:55"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="#E5:55"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="midsp_1.html#T60" target="_self" title="MIDSP_1:th.60">Th60</a></i>
<br/>.= 
 <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c8">c'</font>
<b>by </b><i><a class="txt" href="#E10:55"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="midsp_1.html#T18" target="_self" title="MIDSP_1:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c3">v</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c2">u</font>
<b>by </b><i><a class="txt" href="#E7:55"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="#E9:55"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="midsp_1.html#T60" target="_self" title="MIDSP_1:th.60">Th60</a></i>
;<br/>
<b>hence </b><a NAME="E12:55"/>
<font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c2">u</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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