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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: GRZLOG_1:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="grzlog_1.html#K13" title="GRZLOG_1:func.13">GRZ-formula-set</a><br/>  for <font color="Olive" title="b2">R</font> being   <a href="grzlog_1.html#NM3" title="GRZLOG_1:NM.3">GRZ-rule</a><br/>  for <font color="Olive" title="b3">t</font> being   <a href="grzlog_1.html#NM2" title="GRZLOG_1:NM.2">GRZ-formula</a>  holds <br/>(  not <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">R</font> <a href="grzlog_1.html#R2" title="GRZLOG_1:pred.2">|-</a> <font color="Olive" title="b3">t</font> or <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">A</font> or  ex <font color="Olive" title="b4">S</font> being   <a href="grzlog_1.html#NM5" title="GRZLOG_1:NM.5">GRZ-formula-finset</a> st <br/>( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">S</font>,<font color="Olive" title="b3">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">R</font> &amp; <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">R</font> <a href="grzlog_1.html#R3" title="GRZLOG_1:pred.3">|-</a> <font color="Olive" title="b4">S</font> ) )</div></div>
