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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be  non <a href="pencil_1.html#V13" target="_self">trivial-yielding</a> <a href="pencil_1.html#V16" target="_self">Segre-like</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>;<br/>





<b>assume </b><a NAME="E1:44"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pencil_1.html#K3" target="_self">indx</a> <font color="Maroon">A</font>
 ;<br/>

<b>consider </b><font color="Maroon">j</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font><b> such that </b><br/><a NAME="E3:44"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">I</font>  st <font color="Olive">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font> holds <br/>( not <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> is <a href="realset1.html#V1">trivial</a> )
 <b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:44_1"/>
 <a href="pencil_1.html#K3" target="_self">indx</a> <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">j</font>
 ;<br/><a NAME="E2:44_1"/><b>then </b>
<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="pencil_1.html#K3" target="_self">indx</a> <font color="Maroon">A</font></span>)</span> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="ref" href="pencil_1.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:44_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:44"/>
( not <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="realset1.html#V1">trivial</a> )
 <b>by </b><i>, <a class="ref" href="pencil_1.html#T1" target="_self">Th1</a></i>;<br/>


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