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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">ThDivisibleX1</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: ZMODUL08:30</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> holds <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="zmodul04.html#K5" title="ZMODUL04:func.5">Z_MQ_VectSp</a> <font color="Olive" title="b1">V</font></span>)</span> holds  <font color="Olive" title="b2">v</font> is   <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> ) &amp; (  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> holds  <font color="Olive" title="b2">v</font> is   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="zmodul04.html#K5" title="ZMODUL04:func.5">Z_MQ_VectSp</a> <font color="Olive" title="b1">V</font></span>)</span> ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="zmodul04.html#K5" title="ZMODUL04:func.5">Z_MQ_VectSp</a> <font color="Olive" title="b1">V</font></span>)</span> )</div></div>
