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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E40">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> <font color="Maroon" title="c2">X</font> iff <font color="Olive" title="b1">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> <font color="Maroon" title="c3">Y</font> )
 ;<br/>

<b>given </b><font color="Maroon" title="c4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E3:63"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c4">a</font>
 <b>and </b><br/><a NAME="E4:63"/><i><font color="Green" title="E42">A3</font></i>: 
for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Olive" title="b1">b</font> holds <br/><font color="Maroon" title="c4">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">b</font>
 <b>and </b><br/><a NAME="E5:63"/><i><font color="Green" title="E43">A4</font></i>: 
for <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Olive" title="b1">c</font> &amp; ( for <font color="Olive" title="b2">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Olive" title="b2">b</font> holds <br/><font color="Olive" title="b1">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b2">b</font> ) holds <br/><font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D8" target="_self" title="YELLOW_0:def.8">YELLOW_0:def 8</a><br/>

<b>take </b>
<font color="Maroon" title="c4">a</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D8" target="_self" title="YELLOW_0:def.8">YELLOW_0:def 8</a><br/>

<b>thus </b><a NAME="E6:63"/>
<font color="Maroon" title="c3">Y</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:63"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="yellow_0.html#E3:63"><i><font color="Green" title="E41">A2</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>assume </b><a NAME="E1:63_1"/>
<font color="Maroon" title="c3">Y</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">b</font>
 ;<br/><a NAME="E2:63_1"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:63"><i><font color="Green" title="E40">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:63_1"/>
<font color="Maroon" title="c4">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E4:63"><i><font color="Green" title="E42">A3</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><a NAME="E8:63"/>
<font color="Maroon" title="c3">Y</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">c</font>
 ;<br/>

<a NAME="E9:63"/><b>then </b><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">c</font>
 
<b>by </b><i><a class="txt" href="yellow_0.html#E1:63"><i><font color="Green" title="E40">A1</font></i></a></i>;<br/>
<b>assume </b><a NAME="E10:63"/><i><font color="Green" title="E45">A6</font></i>: 
for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c3">Y</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Olive" title="b1">b</font> holds <br/><font color="Maroon" title="c5">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">b</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/><b>assume </b><a NAME="E1:63_2"/>
<font color="Maroon" title="c2">X</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c6">b</font>
 ;<br/><a NAME="E2:63_2"/><b>then </b>
<font color="Maroon" title="c3">Y</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c6">b</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:63"><i><font color="Green" title="E40">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:63_2"/>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">b</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E10:63"><i><font color="Green" title="E45">A6</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:63"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E5:63"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="yellow_0.html#E9:63"><i><font color="Green" title="E44">A5</font></i></a></i>;<br/>


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