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

<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">W</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c4">L</font> be    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">W</font>;<br/>







<a NAME="E1:51"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c3">W</font>,<font color="Maroon" title="c4">L</font>
 
<b>by </b><i><a class="ref" href="vectsp_5.html#T48" target="_self" title="VECTSP_5:th.48">Th48</a></i>;<br/>
<b>hence </b><a NAME="E2:51"/>
<font color="Maroon" title="c3">W</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c4">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D4" target="_self" title="VECTSP_5:def.4">Def4</a></i>;<br/>

<b>thus </b><a NAME="E3:51"/>
<font color="Maroon" title="c4">L</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c3">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="txt" href="vectsp_5.html#E1:51"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="vectsp_5.html#D4" target="_self" title="VECTSP_5:def.4">Def4</a></i>;<br/>


</div>
