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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:66"/><i><font color="Green">E18</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> #)
 <b>and </b><br/><a NAME="E2:66"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">X</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>  ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Olive">X</font> &amp; ( for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Olive">X</font> holds <br/><font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">y</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D40">WAYBEL_0:def 40</a><br/>

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D40">WAYBEL_0:def 40</a><br/>

<b>consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E4:66"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E5:66"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Olive">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">y</font>
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">z</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">z</font>
;<br/>

<b>thus </b><a NAME="E7:66"/>
<font color="Maroon">z</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font>
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T2">YELLOW_0:2</a></i>;<br/>

<b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>

<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E9:66"/>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E10:66"/><b>then </b>
<font color="Maroon">s</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T2">YELLOW_0:2</a></i>;<br/>
<a NAME="E11:66"/><b>then </b>
<font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E12:66"/>
<font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T1">YELLOW_0:1</a></i>;<br/>


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