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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</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">W</font> being   <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b2">L</font> being   <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Olive" title="b1">W</font> holds  <font color="Olive" title="b1">W</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Olive" title="b2">L</font></span><br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</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"> for <font color="Olive" title="b1">L</font> being   <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Maroon" title="c2">W</font> holds  <font color="Maroon" title="c2">W</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Olive" title="b1">L</font></span><br/><b>let </b><font color="Maroon" title="c3">L</font> be    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Maroon" title="c2">W</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">W</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">L</font></span><br/>





<a NAME="E1:50"/>
<font color="Maroon" title="c1">V</font> <a href="rusub_2.html#R1" title="RUSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c2">W</font>
 
<b>by </b><i><a class="ref" href="rusub_2.html#D5" target="_self" title="RUSUB_2:def.5">Def5</a></i>;<br/>
<a NAME="E2:50"/><b>then </b>
<font color="Maroon" title="c1">V</font> <a href="rusub_2.html#R1" title="RUSUB_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="txt" href="rusub_2.html#E53"><i><font color="Green" title="E36">Lm15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:50"/>
<font color="Maroon" title="c2">W</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="rusub_2.html#D5" target="_self" title="RUSUB_2:def.5">Def5</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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