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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>;<br/><b>let </b><font color="Maroon" title="c2">W</font> be    <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="c3">L</font> be    <a href="rlsub_2.html#M1" title="RLSUB_2:mode.1">Linear_Compl</a> of <font color="Maroon" title="c2">W</font>;<br/>





<a NAME="E1:67"/>
<font color="Maroon" title="c1">V</font> <a href="rlsub_2.html#R1" title="RLSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c2">W</font>,<font color="Maroon" title="c3">L</font>
 
<b>by </b><i><a class="ref" href="rlsub_2.html#T43" target="_self" title="RLSUB_2:th.43">Th43</a></i>;<br/>
<b>hence </b><a NAME="E2:67"/>
for <font color="Olive" title="b1">v</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v</font> <a href="rlsub_2.html#K4" title="RLSUB_2:func.4">|--</a> <font color="Maroon" title="c2">W</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">v</font> <a href="rlsub_2.html#K4" title="RLSUB_2:func.4">|--</a> <font color="Maroon" title="c2">W</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#D6" target="_self" title="RLSUB_2:def.6">Def6</a></i>;<br/>


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