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<div><span class="kw">theorem </span><a NAME="T59"><span class="comment"><font color="firebrick">:: ZMODUL02:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V</font>  st  not <font color="Olive" title="b1">R</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  &amp; <font color="Olive" title="b2">V</font> is  <a href="zmodul01.html#V1" title="ZMODUL01:attr.1">Mult-cancelable</a>  holds <br/>( <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  iff <font color="Olive" title="b3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">V</font> )</div></div>
