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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th62</font></span>: <a NAME="T62"><span class="comment"><font color="firebrick">:: ZMODUL02:62</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">v1</font>, <font color="Olive" title="b3">v2</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b1">V</font> is  <a href="zmodul01.html#V1" title="ZMODUL01:attr.1">Mult-cancelable</a>  holds <br/>( <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">v2</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> is  <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  iff ( <font color="Olive" title="b3">v2</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="b1">V</font> &amp; (  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</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="b5">b</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> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds <br/><font color="Olive" title="b5">b</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b2">v1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">v2</font> ) ) )</div></div>
