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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: QUOFIELD:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">u</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="quofield.html#K7" title="QUOFIELD:func.7">Quot.</a> <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="quofield.html#K11" title="QUOFIELD:func.11">q0.</a> <font color="Olive" title="b1">I</font> holds <br/>(  <a href="quofield.html#K9" title="QUOFIELD:func.9">qmult</a> (<font color="Olive" title="b2">u</font>,<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">qmultinv</a> <font color="Olive" title="b2">u</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">q1.</a> <font color="Olive" title="b1">I</font> &amp;  <a href="quofield.html#K9" title="QUOFIELD:func.9">qmult</a> (<span class="p1">(<span class="default"><a href="quofield.html#K14" title="QUOFIELD:func.14">qmultinv</a> <font color="Olive" title="b2">u</font></span>)</span>,<font color="Olive" title="b2">u</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quofield.html#K12" title="QUOFIELD:func.12">q1.</a> <font color="Olive" title="b1">I</font> )</div></div>
