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<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">VS</font> be  <a href="vectsp_1.html#V11">strict</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">VS</font>;<br/>







<b>assume </b><a NAME="E1:15"/><i><font color="Green">E24</font></i>: 
( not <font color="Maroon">S</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">S</font> is <a href="vectsp_4.html#V1">lineary-closed</a> )
 ;<br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="rlvect_1.html#R1">in</a>  <a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">S</font>
 ;<br/>

<b>consider </b><font color="Maroon">W</font> being  <a href="vectsp_1.html#V11">strict</a>  <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">VS</font><b> such that </b><br/><a NAME="E4:15"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>
 <b>by </b><i>, <a class="ref" href="vectsp_4.html#T42">VECTSP_4:42</a></i>;<br/>
<a NAME="E5:15"/>
 <a href="vectsp_7.html#K1">Lin</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font>
 
<b>by </b><i>, <a class="ref" href="vectsp_7.html#T16">VECTSP_7:16</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 <b>by </b><i>, , <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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