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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">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>





<a NAME="E1:45"/>
( (  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> implies <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> ) &amp; ( <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> implies  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> ) &amp; ( <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> implies <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> ) &amp; ( <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> implies <font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W</font> ) )
 
<b>by </b><i>, <a class="ref" href="rusub_1.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E2:45"/>
(  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R2">in</a> <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> iff <font color="Maroon">v</font> <a href="rusub_1.html#K3" target="_self">+</a> <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font> )
 ;<br/>


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