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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u</font> being    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font>  ex <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> st <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>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">v</font> being    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> st <font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">a</font> =  the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E2:53"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<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> ( the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c4">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T35" target="_self" title="MIDSP_1:th.35">Th55</a></span>;<br/>
<font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <span class="p1">(<span class="default"><a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> (<font color="Maroon" title="c4">b</font>, the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>)</span>)</span> = 
 <a href="midsp_1.html#K10" title="MIDSP_1:func.10">vect</a> ( the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>, the   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="midsp_1.html#T40" target="_self" title="MIDSP_1:th.40">Th60</a></span>
<br/>.= 
 <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T32" target="_self" title="MIDSP_1:th.32">Th50</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:53"/>
 ex <font color="Olive" title="b1">v</font> being    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> st <font color="Maroon" title="c2">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_1.html#K8" title="MIDSP_1:func.8">ID</a> <font color="Maroon" title="c1">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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