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<div>:: <span class="kw">deftheorem </span>   defines <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a> <a onclick="hs(this)" href="javascript:()">PROOFS_1:def 8 : <br/></a><span> for <font color="Olive" title="b1">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b3">S</font> being   <a href="proofs_1.html#NM3" title="PROOFS_1:NM.3">Formula-finset</a> holds <br/> ( <font color="Olive" title="b3">S</font> is <font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#V3" title="PROOFS_1:attr.3">-derivable</a>  iff  ex <font color="Olive" title="b4">P</font> being   <a href="proofs_1.html#NM4" title="PROOFS_1:NM.4">Formula-sequence</a> st <br/>( <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="proofs_1.html#K1" title="PROOFS_1:func.1">rng</a> <font color="Olive" title="b4">P</font> &amp; <font color="Olive" title="b4">P</font> is <font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#V2" title="PROOFS_1:attr.2">-correct</a>  ) );<br/></span></div>
