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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: ZMODUL05:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st  <a href="zmodul03.html#K1" title="ZMODUL03:func.1">rank</a> <font color="Olive" title="b1">V</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">n</font> holds <br/><font color="Olive" title="b2">n</font> <a href="zmodul05.html#K1" title="ZMODUL05:func.1">Submodules_of</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </div></div>
