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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: QUOFIELD:45</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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K19" title="QUOFIELD:func.19">the_Field_of_Quotients</a> <font color="Olive" title="b1">I</font></span>)</span>  st <font color="Olive" title="b2">u</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> <span class="p1">(<span class="default"><a href="quofield.html#K19" title="QUOFIELD:func.19">the_Field_of_Quotients</a> <font color="Olive" title="b1">I</font></span>)</span> holds <br/> ex <font color="Olive" title="b3">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K19" title="QUOFIELD:func.19">the_Field_of_Quotients</a> <font color="Olive" title="b1">I</font></span>)</span> st <font color="Olive" title="b2">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="quofield.html#K19" title="QUOFIELD:func.19">the_Field_of_Quotients</a> <font color="Olive" title="b1">I</font></span>)</span></div></div>
