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<b>let </b><font color="Maroon">R</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">R</font>;<br/>



<b>set </b><font color="Maroon">W</font> =  <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font>;<br/>
<b>reconsider </b><font color="Maroon">B'</font> =  <a href="subset_1.html#K1">{}</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <b>by </b><i><a class="ref" href="subset_1.html#T4">SUBSET_1:4</a></i>;<br/>
<a NAME="E2:18"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">B'</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K1">{}</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>
 
;<br/>
<a NAME="E3:18"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">B'</font> is <a href="lmod_5.html#V1">linearly-independent</a>
 
<b>by </b><i><a class="ref" href="lmod_5.html#T4">LMOD_5:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">V'</font> = <font color="Maroon">V</font> as    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font> <b>by </b><i><a class="ref" href="vectsp_4.html#T32">VECTSP_4:32</a></i>;<br/>
<a NAME="E5:18"/>
 <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V'</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1">(0).</a> <span class="p1">(<span class="default"><a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T48">VECTSP_4:48</a></i>;<br/>
<a NAME="E6:18"/><b>then </b>
 <a href="mod_3.html#K1" target="_self">Lin</a> <font color="Maroon">B'</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:18"/><b>then </b>
<font color="Maroon">B'</font> is <a href="mod_3.html#V1" target="_self">base</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:18"/>
 <a href="vectsp_4.html#K1">(0).</a> <font color="Maroon">V</font> is <a href="mod_3.html#V2" target="_self">free</a>
 <b>by </b><i/>;<br/>


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