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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:23_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   ex <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">a</font> &amp; ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Olive">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D12">LATTICE3:def 12</a><br/>

<b>then consider </b><font color="Maroon">a0</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:23_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a0</font>
 <b>and </b><br/><a NAME="E4:23_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st  <a href="xboole_0.html#K1">{}</a>  <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Maroon">a0</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b</font>
 ;<br/>
<b>consider </b><font color="Maroon">a1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E6:23_1_1"/><i><font color="Green">E30</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a1</font>
 <b>and </b><br/><a NAME="E7:23_1_1"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Maroon">a1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">a0</font> = <font color="Maroon">a0</font>, <font color="Maroon">a1</font> = <font color="Maroon">a1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" target="_self">YELLOW_0:def 4</a>,<a class="ref" href="yellow_0.html#D6" target="_self">YELLOW_0:def 6</a>
<div class="add"><b>take </b><font color="Maroon">a0</font> = <font color="Maroon">a0</font>;<br/><b>thus </b><a NAME="E1:23_1_1_1"/>
<font color="Maroon">a0</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a><br/>

<b>assume </b><a NAME="E1:23_1_1_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E3:23_1_1_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:23_1_1_1_1"/>
<font color="Maroon">a0</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div></div>
<b>end;</b></div>

<b>take </b>
<font color="Maroon">a1</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" target="_self">YELLOW_0:def 5</a><br/>

<b>thus </b><a NAME="E10:23_1_1"/>
<font color="Maroon">a1</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


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