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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E11">Def3</font></span>   defines <a href="yellow_8.html#V3" title="YELLOW_8:attr.3">irreducible</a> <a onclick="hs(this)" href="javascript:()">YELLOW_8:def 3 : <br/></a><span> for <font color="Olive" title="b1">T</font> being    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <font color="Olive" title="b2">S</font> is  <a href="yellow_8.html#V3" title="YELLOW_8:attr.3">irreducible</a>  iff (  not <font color="Olive" title="b2">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; (  for <font color="Olive" title="b3">S1</font>, <font color="Olive" title="b4">S2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b3">S1</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b4">S2</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  &amp; <font color="Olive" title="b2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">S1</font> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Olive" title="b4">S2</font> &amp;  not <font color="Olive" title="b3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">S</font> holds <br/><font color="Olive" title="b4">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">S</font> ) ) );<br/></span></div>
