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<b>let </b><font color="Maroon">V</font> be   <a href="clvect_1.html#NM2">ComplexLinearSpace</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="clvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="clvect_1.html#M1" target="_self">Subspace</a> of <font color="Maroon">V</font>;<br/>





<a NAME="E1:83"/>
( (  <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="clvect_1.html#K4" 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="clvect_1.html#K4" 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="clvect_1.html#K4" 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="clvect_1.html#K4" 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="clvect_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:83"/>
(  <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="clvect_1.html#K4" target="_self">+</a> <font color="Maroon">W</font> iff <font color="Maroon">v</font> <a href="clvect_1.html#K4" 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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