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<b>let </b><font color="Maroon" title="c1">P1</font>, <font color="Maroon" title="c2">P2</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">P1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">P2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">P2</font> #)
 ;<br/>

<b>thus </b><a NAME="E2:22"/>
( <font color="Maroon" title="c1">P1</font> is <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> implies <font color="Maroon" title="c2">P2</font> is <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P1</font><b> such that </b><a NAME="E2:22_1"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" target="_self" title="YELLOW_0:def.4">YELLOW_0:def 4</a><br/>

<b>reconsider </b><font color="Maroon" title="c4">y</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">P2</font> <b>by </b><i><a class="txt" href="yellow_0.html#E1:22"><i><font color="Green" title="E14">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">y</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" target="_self" title="YELLOW_0:def.4">YELLOW_0:def 4</a><br/>

<b>thus </b><a NAME="E4:22_1"/>
<font color="Maroon" title="c4">y</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">P2</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:22"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="yellow_0.html#E2:22_1"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="yellow_0.html#T2" target="_self" title="YELLOW_0:th.2">Th2</a></i>;<br/>


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

<b>given </b><font color="Maroon" title="c3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P1</font><b> such that </b><a NAME="E4:22"/><i><font color="Green" title="E15">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#NR4" title="LATTICE3:NR.4">is_&gt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" target="_self" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<b>reconsider </b><font color="Maroon" title="c4">y</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">P2</font> <b>by </b><i><a class="txt" href="yellow_0.html#E1:22"><i><font color="Green" title="E14">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">y</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" target="_self" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<b>thus </b><a NAME="E6:22"/>
<font color="Maroon" title="c4">y</font> <a href="lattice3.html#NR4" title="LATTICE3:NR.4">is_&gt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">P2</font>
 <b>by </b><i><a class="txt" href="yellow_0.html#E1:22"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="yellow_0.html#E4:22"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="yellow_0.html#T2" target="_self" title="YELLOW_0:th.2">Th2</a></i>;<br/>


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