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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>;<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>;<br/><b>let </b><font color="Maroon" title="c3">u</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>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W</font>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W</font>
 ;<br/>

<a NAME="E3:18"/>
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W</font>
 
<b>by </b><i><a class="txt" href="rusub_1.html#E2:18"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="rusub_1.html#T16" target="_self" title="RUSUB_1:th.16">Th16</a></i>;<br/>
<a NAME="E4:18"/><b>then </b>
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W</font>
 
<b>by </b><i><a class="txt" href="rusub_1.html#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="rusub_1.html#T14" target="_self" title="RUSUB_1:th.14">Th14</a></i>;<br/>
<b>hence </b><a NAME="E5:18"/>
<font color="Maroon" title="c3">u</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">v</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">W</font>
 ;<br/>


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