<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>







<span class="kw">assume </span><a NAME="E1:17"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:17"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:17"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></span>; <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">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/>

<span class="kw">thus </span><a NAME="E4:17"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="analoaf.html#T22" title="ANALOAF:th.22">ANALOAF:22</a></span>; <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">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="E5:17"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="analoaf.html#T22" title="ANALOAF:th.22">ANALOAF:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:17"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</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/>


</div>
