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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: RINGFRAC:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</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="b2">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="c0sp1.html#V3" title="C0SP1:attr.3">multiplicatively-closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ringfrac.html#K6" title="RINGFRAC:func.6">Frac</a> <font color="Olive" title="b2">S</font>  st  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> holds <br/><font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font> <a href="ringfrac.html#R1" title="RINGFRAC:pred.1">Fr_Eq</a> <font color="Olive" title="b2">S</font></div></div>
