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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: RINGFRAC:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">R1</font> being   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">R1</font><br/>  for <font color="Olive" title="b4">u</font> being   <a href="ring_2.html#NM3" title="RING_2:NM.3">Unit</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b5">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b3">f</font> is  <a href="quofield.html#NV1" title="QUOFIELD:NV.1">RingHomomorphism</a>  holds <br/>( <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">u</font> is   <a href="ring_2.html#NM3" title="RING_2:NM.3">Unit</a> of <font color="Olive" title="b2">R1</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">u</font></span>)</span> <a href="ringfrac.html#NK5" title="RINGFRAC:NK.5">["]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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"><font color="Olive" title="b4">u</font> <a href="ringfrac.html#NK5" title="RINGFRAC:NK.5">["]</a></span>)</span> )</div></div>
