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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: FOMODEL2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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>  st  <a href="fomodel2.html#K29" title="FOMODEL2:func.29">Depth</a> <font color="Olive" title="b3">phi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/>( ( <font color="Olive" title="b3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  implies <font color="Olive" title="b3">phi</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">m</font> <a href="fomodel2.html#K33" title="FOMODEL2:func.33">-ExFormulasOf</a> <font color="Olive" title="b2">S</font> ) &amp; ( <font color="Olive" title="b3">phi</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">m</font> <a href="fomodel2.html#K33" title="FOMODEL2:func.33">-ExFormulasOf</a> <font color="Olive" title="b2">S</font> implies <font color="Olive" title="b3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  ) &amp; (  not <font color="Olive" title="b3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  implies <font color="Olive" title="b3">phi</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">m</font> <a href="fomodel2.html#K32" title="FOMODEL2:func.32">-NorFormulasOf</a> <font color="Olive" title="b2">S</font> ) &amp; ( <font color="Olive" title="b3">phi</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">m</font> <a href="fomodel2.html#K32" title="FOMODEL2:func.32">-NorFormulasOf</a> <font color="Olive" title="b2">S</font> implies  not <font color="Olive" title="b3">phi</font> is  <a href="fomodel2.html#V5" title="FOMODEL2:attr.5">exal</a>  ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="fomodel2.html#E74"><span class="lab"><font color="Green" title="E56">Lm27</font></span></a>, <a class="txt" href="fomodel2.html#E76"><span class="lab"><font color="Green" title="E58">Lm29</font></span></a></span>;<br/></div></div>
