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<b>let </b><font color="Maroon">V</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">W1</font> be  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>, <font color="Maroon">W2</font> be  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">C1</font> be    <a href="rusub_1.html#M2" target="_self">Coset</a> of <font color="Maroon">W1</font>;<br/><b>let </b><font color="Maroon">C2</font> be    <a href="rusub_1.html#M2" target="_self">Coset</a> of <font color="Maroon">W2</font>;<br/>







<a NAME="E1:68"/><i><font color="Green">E19</font></i>: 
 ex <font color="Olive">v1</font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> st <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Olive">v1</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:68"/>
 ex <font color="Olive">v2</font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> st <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> <font color="Olive">v2</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:68"/>
( <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font> implies <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> )
 <b>by </b><i>, </i>;<br/>


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