<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="fomodel4.html#V9" title="FOMODEL4:attr.9">-provable</a> <a onclick="hs(this)" href="javascript:()">FOMODEL4:def 13 : <br/></a><span> for <font color="Olive" title="b1">S</font> being   <a href="fomodel1.html#NM2" title="FOMODEL1:NM.2">Language</a><br/>  for <font color="Olive" title="b2">D</font> being   <a href="fomodel4.html#NM2" title="FOMODEL4:NM.2">RuleSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">phi</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b4">phi</font> is <font color="Olive" title="b3">X</font>,<font color="Olive" title="b2">D</font> <a href="fomodel4.html#V9" title="FOMODEL4:attr.9">-provable</a>  iff ( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">phi</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-derivable</a>  or  ex <font color="Olive" title="b5">seqt</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b5">seqt</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">X</font> &amp; <font color="Olive" title="b5">seqt</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">phi</font> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b5">seqt</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <font color="Olive" title="b2">D</font> <a href="fomodel4.html#V8" title="FOMODEL4:attr.8">-derivable</a>  ) ) );<br/></span></div>
