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<b>let </b><font color="Maroon">P1</font> be    <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">P2</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E24</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">P1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">P1</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">P2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">P2</font> #)
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E29</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">P1</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">P1</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>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D12">LATTICE3:def 12</a><br/>

<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P1</font><b> such that </b><br/><a NAME="E4:9"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E5:9"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P1</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Maroon">a</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">a'</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P2</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">a'</font>
;<br/>

<b>thus </b><a NAME="E7:9"/>
<font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a'</font>
 <b>by </b><i>, , </i>;<br/>

<b>let </b><font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P2</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">P1</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E9:9"/>
<font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">b'</font>
 ;<br/>

<a NAME="E10:9"/><b>then </b>
<font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">b</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:9"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E12:9"/>
<font color="Maroon">a'</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b'</font>
 <b>by </b><i>, </i>;<br/>


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