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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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">y</font>, <font color="Olive" title="b3">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">v</font> holds <br/>( <font color="Olive" title="b3">v</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">u</font> &amp; <font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> &amp; <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Olive" title="b1">u</font>,<font color="Olive" title="b3">v</font> )</span><br/><b>let </b><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</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>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> implies ( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> ) )</span><br/>







<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">u</font> &amp; <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> )</span><br/>

<a NAME="E2:15"/><b>then </b>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">u</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">y</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/>
<b>hence </b><a NAME="E3:15"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c2">u</font>
 <b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>; <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>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> &amp; <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font> )</span><br/>

<b>thus </b><a NAME="E4:15"/>
<font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font>
 <b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="analoaf.html#T22" title="ANALOAF:th.22">ANALOAF:22</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font></span><br/>

<a NAME="E5:15"/>
<font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c3">y</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c2">u</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="analoaf.html#T22" title="ANALOAF:th.22">ANALOAF:22</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">v</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c2">u</font>,<font color="Maroon" title="c4">v</font>
 <b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</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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