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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ZMODUL06:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">W</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font>  ex <font color="Olive" title="b3">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b3">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">W</font> &amp; <font color="Olive" title="b3">A</font> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  &amp;  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Olive" title="b2">W</font> )</div></div>
