<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> <a href="yellow_4.html#K2" title="YELLOW_4:func.2">"\/"</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="yellow_4.html#K2" title="YELLOW_4:func.2">"\/"</a> <font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c3">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> or <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="yellow_4.html#K2" title="YELLOW_4:func.2">"\/"</a> <font color="Maroon" title="c2">A</font> )</span><br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="yellow_4.html#K2" title="YELLOW_4:func.2">"\/"</a> <font color="Maroon" title="c2">A</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">A1</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="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">q1</font> = <font color="Maroon" title="c3">q</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">A1</font> <b>by </b><i><a class="txt" href="yellow_4.html#E1:16"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>
<a NAME="E4:16"/>
<font color="Maroon" title="c5">q1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">q1</font>
 
;<br/>
<a NAME="E5:16"/><b>then </b>
<font color="Maroon" title="c5">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">q1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T24" title="YELLOW_0:th.24">YELLOW_0:24</a></i>;<br/>
<b>hence </b><a NAME="E6:16"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="yellow_4.html#K2" title="YELLOW_4:func.2">"\/"</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
