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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">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">Subspace</a> of <font color="Maroon">V</font>;<br/>



<a NAME="E1:39"/>
( ( <font color="Maroon">W1</font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> implies <font color="Maroon">W1</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> ) &amp; ( <font color="Maroon">W1</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> implies <font color="Maroon">W1</font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> ) &amp; ( <font color="Maroon">W1</font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> implies <font color="Maroon">W1</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> ) &amp; ( <font color="Maroon">W1</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> implies <font color="Maroon">W1</font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:39"/>
( <font color="Maroon">W1</font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font> iff <font color="Maroon">W1</font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> )
 ;<br/>


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