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<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: RING_2:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="vectsp_1.html#V13" title="VECTSP_1:attr.13">additive</a>   <a href="group_6.html#V1" title="GROUP_6:attr.1">multiplicative</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">F</font> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">E</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> <font color="Olive" title="b2">F</font> iff <font color="Olive" title="b3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">E</font> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">F</font></span>)</span> )</div></div>
