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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E102">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: FOMODEL4:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Z</font> being    <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">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">X</font> being   <a href="funct_1.html#V4" title="FUNCT_1:attr.4">functional</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">num</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="fomodel2.html#K40" title="FOMODEL2:func.40">ExFormulasOf</a> <font color="Olive" title="b2">S</font></span>)</span>  st <font color="Olive" title="b3">D</font> is  <a href="fomodel4.html#V7" title="FOMODEL4:attr.7">isotone</a>  &amp;  <a href="fomodel4.html#K25" title="FOMODEL4:func.25">R#1</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp;  <a href="fomodel4.html#K35" title="FOMODEL4:func.35">R#8</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp;  <a href="fomodel4.html#K26" title="FOMODEL4:func.26">R#2</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp;  <a href="fomodel4.html#K32" title="FOMODEL4:func.32">R#5</a> <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">D</font> &amp; <span class="p1">(<span class="default"><a href="fomodel1.html#K16" title="FOMODEL1:func.16">LettersOf</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="fomodel0.html#K21" title="FOMODEL0:func.21">SymbolsOf</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="fomodel1.html#K1" title="FOMODEL1:func.1">AllSymbolsOf</a> <font color="Olive" title="b2">S</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span></span>)</span> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  &amp; <font color="Olive" title="b4">X</font> <a href="fomodel4.html#NK47" title="FOMODEL4:NK.47">addw</a> (<font color="Olive" title="b3">D</font>,<font color="Olive" title="b5">num</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Z</font> &amp; <font color="Olive" title="b1">Z</font> is <font color="Olive" title="b3">D</font> <a href="fomodel4.html#NV18" title="FOMODEL4:NV.18">-consistent</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b5">num</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fomodel2.html#K40" title="FOMODEL2:func.40">ExFormulasOf</a> <font color="Olive" title="b2">S</font> holds <br/><font color="Olive" title="b1">Z</font> is <font color="Olive" title="b2">S</font> <a href="fomodel4.html#V14" title="FOMODEL4:attr.14">-witnessed</a> </div></div>
