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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: PROOFS_1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="proofs_1.html#L1" title="PROOFS_1:struct.1">ProofSystem</a> <br/>  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">P</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Olive" title="b2">a</font> iff  for <font color="Olive" title="b3">X</font> being  <font color="Olive">b<sub>1</sub></font> <a href="proofs_1.html#V19" title="PROOFS_1:attr.19">-closed</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">X</font> )</div></div>
