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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:39"/>
( ( <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 
<b>by </b><i><a class="ref" href="rusub_2.html#T8" target="_self">Th8</a>, <a class="ref" href="rusub_2.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E2:39"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>


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