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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">ThDivisible1</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: ZMODUL08:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul06.html#V3" title="ZMODUL06:attr.3">torsion-free</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul08.html#K2" title="ZMODUL08:func.2">DivisibleMod</a> <font color="Olive" title="b1">V</font></span>)</span><br/>  for <font color="Olive" title="b3">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  st <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b4">u</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul08.html#K2" title="ZMODUL08:func.2">DivisibleMod</a> <font color="Olive" title="b1">V</font></span>)</span> st <font color="Olive" title="b3">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font></div></div>
