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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">W</font>, <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</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">W1</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> &amp; <font color="Olive" title="b1">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Olive" title="b3">W2</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> holds <br/><font color="Olive" title="b2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">W2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">W</font>, <font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</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">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c3">W1</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> &amp; <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c4">W2</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> implies <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:91"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
( <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c3">W1</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> &amp; <font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c4">W2</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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c2">W</font>, <font color="Maroon" title="c6">y1</font> = <font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c7">y2</font> = <font color="Maroon" title="c4">W2</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/>
<font color="Maroon" title="c5">x</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c6">y1</font> = 
<font color="Maroon" title="c2">W</font> <a href="midsp_1.html#K13" title="MIDSP_1:func.13">+</a> <font color="Maroon" title="c4">W2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:91"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="midsp_1.html#D14" target="_self" title="MIDSP_1:def.14">Def14</a></span>
<br/>.= 
<font color="Maroon" title="c5">x</font> <a href="midsp_1.html#K9" title="MIDSP_1:func.9">+</a> <font color="Maroon" title="c7">y2</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/>
<span class="kw">hence </span><a NAME="E4:91"/>
<font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T67" target="_self" title="MIDSP_1:th.67">Th67</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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