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<a NAME="E1:37_1_1"/>
<font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_2.html#K6" title="MSUALG_2:func.6">SubSort</a> <font color="Maroon" title="c2">OU0</font> : <font color="Olive" title="b1">x</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon" title="c4">e1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_2.html#K6" title="MSUALG_2:func.6">SubSort</a> <font color="Maroon" title="c2">OU0</font><b> such that </b><br/><a NAME="E3:37_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e1</font> &amp; <font color="Maroon" title="c4">e1</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">e2</font> =  <a href="msualg_2.html#K7" title="MSUALG_2:func.7">@</a> <font color="Maroon" title="c4">e1</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font> <b>by </b><i><a class="txt" href="osalg_2.html#E3:37_1_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E5:37_1_1"/>
<font color="Maroon" title="c5">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E3:37_1_1"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:37_1_1"/>
<font color="Maroon" title="c3">e</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font>
 ; <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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