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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: REALALG1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">S</font> being    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of <font color="Olive" title="b1">R</font> holds   <a href="realalg1.html#NK5" title="REALALG1:NK.5">QS</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="realalg1.html#NK5" title="REALALG1:NK.5">QS</a> <font color="Olive" title="b1">R</font></div></div>
