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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E72">Th13</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: FOMODEL3:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">U</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b3">phi</font> being   <a href="fomodel2.html#V4" title="FOMODEL2:attr.4">wff</a>  <a href="fomodel1.html#NM3" title="FOMODEL1:NM.3">string</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">I1</font>, <font color="Olive" title="b5">I2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">U</font> <a href="fomodel2.html#K15" title="FOMODEL2:func.15">-InterpretersOf</a> <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b4">I1</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">phi</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b2">S</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">I2</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">phi</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="fomodel1.html#K37" title="FOMODEL1:func.37">OwnSymbolsOf</a> <font color="Olive" title="b2">S</font></span>)</span></span>)</span> holds <br/><font color="Olive" title="b4">I1</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-TruthEval</a> <font color="Olive" title="b3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">I2</font> <a href="fomodel2.html#K25" title="FOMODEL2:func.25">-TruthEval</a> <font color="Olive" title="b3">phi</font></div></div>
