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

<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a>  <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c4">C1</font> be    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c2">W1</font>;<br/><b>let </b><font color="Maroon" title="c5">C2</font> be    <a href="rlsub_1.html#M2" title="RLSUB_1:mode.2">Coset</a> of <font color="Maroon" title="c3">W2</font>;<br/>







<a NAME="E1:74"/><i><font color="Green" title="E53">A1</font></i>: 
 ex <font color="Olive" title="b1">v1</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="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c2">W1</font>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D6" target="_self" title="RLSUB_1:def.6">Def6</a></i>;<br/>
<a NAME="E2:74"/>
 ex <font color="Olive" title="b1">v2</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="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Maroon" title="c3">W2</font>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D6" target="_self" title="RLSUB_1:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E3:74"/>
( <font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C2</font> implies <font color="Maroon" title="c2">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> )
 <b>by </b><i><a class="txt" href="rlsub_1.html#E1:74"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="rlsub_1.html#T85" target="_self" title="RLSUB_1:th.85">Th85</a></i>;<br/>


</div>
