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<b>let </b><font color="Maroon" title="c1">Omega</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font></span><br/>

<a NAME="E1:76"/>
(  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> is <a href="prob_3.html#V2" title="PROB_3:attr.2">non-decreasing-closed</a> &amp;  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> is <a href="prob_3.html#V3" title="PROB_3:attr.3">non-increasing-closed</a> )
 
<b>by </b><i><a class="ref" href="prob_3.html#T73" target="_self" title="PROB_3:th.73">Th73</a></i>;<br/>
<b>hence </b><a NAME="E2:76"/>
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> <font color="Maroon" title="c1">Omega</font> is    <a href="prob_3.html#M2" title="PROB_3:mode.2">MonotoneClass</a> of <font color="Maroon" title="c1">Omega</font>
 <b>by </b><i><a class="ref" href="prob_3.html#D14" target="_self" title="PROB_3:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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