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<div class="add">

<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><a NAME="E1:22"/><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> #)
 ;<br/>

<b>thus </b><a NAME="E2:22"/>
( <font color="Maroon">P1</font> is <a href="yellow_0.html#V1" target="_self">lower-bounded</a> implies <font color="Maroon">P2</font> is <a href="yellow_0.html#V1" target="_self">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">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P1</font><b> such that </b><a NAME="E1:22_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">P1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" target="_self">YELLOW_0:def 4</a><br/>

<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</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">y</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D4" target="_self">YELLOW_0:def 4</a><br/>

<b>thus </b><a NAME="E3:22_1"/>
<font color="Maroon">y</font> <a href="lattice3.html#R1">is_&lt;=_than</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">P2</font>
 <b>by </b><i>, , </i>;<br/>


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

<b>given </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P1</font><b> such that </b><a NAME="E3:22"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</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">P1</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>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</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">y</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="E5:22"/>
<font color="Maroon">y</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">P2</font>
 <b>by </b><i>, , </i>;<br/>


</div>
