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<b>consider </b><font color="Maroon" title="c2">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">F</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">A</font> = <font color="Maroon" title="c2">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="setfam_1.html#D9" title="SETFAM_1:def.9">SETFAM_1:def 9</a></i>;<br/>
<a NAME="E3:23_1_1"/>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c3">A</font>
 
;<br/>
<b>hence </b><a NAME="E4:23_1_1"/>
not  <a href="supinf_1.html#K5" title="SUPINF_1:func.5">SUP</a> <font color="Maroon" title="c1">F</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="supinf_1.html#D19" target="_self" title="SUPINF_1:def.19">Def19</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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