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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</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> holds  <font color="Olive" title="b1">u1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b1">u1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">u1</font>, <font color="Maroon" title="c3">v1</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">u1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c2">u1</font></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">u</font> = <font color="Maroon" title="c2">u1</font>, <font color="Maroon" title="c5">v</font> = <font color="Maroon" title="c3">v1</font> as    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T71" target="_self" title="MIDSP_1:th.71">Th71</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c2">u1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c3">v1</font> = 
<font color="Maroon" title="c4">u</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c5">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#D14" target="_self" title="MIDSP_1:def.14">Def14</a></span>
<br/>.= 
<font color="Maroon" title="c5">v</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c4">u</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T66" target="_self" title="MIDSP_1:th.66">Th66</a></span>
<br/>.= 
<font color="Maroon" title="c3">v1</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c2">u1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#D14" target="_self" title="MIDSP_1:def.14">Def14</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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