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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">W</font> be    <a href="rusub_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">w1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">W</font>, <font color="Maroon">w2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">W</font>;<br/>







<b>assume </b><a NAME="E1:6"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w1</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">ww1</font> = <font color="Maroon">w1</font>, <font color="Maroon">ww2</font> = <font color="Maroon">w2</font> as   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> <b>by </b><i/>;<br/>
<a NAME="E3:6"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">ww1</font>,<font color="Maroon">ww2</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:6"/>
<font color="Maroon">w1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">w2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">w1</font>,<font color="Maroon">w2</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">w1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">w2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">u</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


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