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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">W</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font>  ex <font color="Olive" title="b2">T</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> st <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b2">T</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/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <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">  ex <font color="Olive" title="b1">T</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> st <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b1">T</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/>



<b>reconsider </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">W</font> as    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> <b>by </b><i><a class="ref" href="midsp_1.html#T71" target="_self" title="MIDSP_1:th.71">Th71</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">y</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="E3:65"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c4">y</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>
 <b>by </b><i><a class="ref" href="midsp_1.html#T65" target="_self" title="MIDSP_1:th.65">Th65</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">T</font> = <font color="Maroon" title="c4">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> <b>by </b><i><a class="ref" href="midsp_1.html#T71" target="_self" title="MIDSP_1:th.71">Th71</a></i>;<br/>
<a NAME="E5:65"/>
<font color="Maroon" title="c3">x</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c5">T</font>
 
<b>by </b><i><a class="ref" href="midsp_1.html#D14" target="_self" title="MIDSP_1:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E6:65"/>
 ex <font color="Olive" title="b1">T</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="midsp_1.html#K12" title="MIDSP_1:func.12">setvect</a> <font color="Maroon" title="c1">M</font> st <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b1">T</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>
 <b>by </b><i><a class="txt" href="#E3:65"><i><font color="Green" title="E47">A1</font></i></a></i>; <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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