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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> 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="E1:12"/>
 <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rusub_1.html#T33">RUSUB_1:33</a></i>;<br/>
<a NAME="E2:12"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rusub_1.html#D1">RUSUB_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:12"/>
<span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rusub_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>;<br/>

<b>hence </b><a NAME="E4:12"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rusub_2.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>


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