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<b>let </b><font color="Maroon" title="c1">R1</font>, <font color="Maroon" title="c2">R2</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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">R1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</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">R2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font> #) implies for <font color="Olive" title="b1">D</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c1">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c2">R2</font> )</span><br/>

<b>assume </b><a NAME="E1:84"/><i><font color="Green" title="E54">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">R1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</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">R2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font> #)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c1">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c2">R2</font></span><br/>

<b>let </b><font color="Maroon" title="c3">D</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">R2</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">b</font> =  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R2</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a></i>;<br/>
<a NAME="E3:84"/><i><font color="Green" title="E55">A2</font></i>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">R2</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17" title="YELLOW_0:th.17">YELLOW_0:17</a></i>;<br/>
<a NAME="E4:84"/><i><font color="Green" title="E56">A3</font></i>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17" title="YELLOW_0:th.17">YELLOW_0:17</a></i>;<br/>
<a NAME="E5:84"/><b>then </b>
<font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D10" title="YELLOW_0:def.10">YELLOW_0:def 10</a></i>;<br/>
<a NAME="E6:84"/><b>then </b><i><font color="Green" title="E57">A4</font></i>: 
<font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="waybel11.html#E60"><i><font color="Green" title="E51">Lm11</font></i></a></i>;<br/>
<a NAME="E7:84"/>
for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R2</font>  st <font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Olive" title="b1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">a</font> implies <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c6">a'</font> = <font color="Maroon" title="c5">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R1</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a></i>;<br/>
<b>assume </b><a NAME="E2:84_1"/>
<font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c5">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font></span><br/>

<a NAME="E3:84_1"/><b>then </b>
<font color="Maroon" title="c3">D</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c6">a'</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="waybel11.html#E60"><i><font color="Green" title="E51">Lm11</font></i></a></i>;<br/>
<a NAME="E4:84_1"/><b>then </b>
<font color="Maroon" title="c6">a'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E4:84"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="yellow_0.html#D10" title="YELLOW_0:def.10">YELLOW_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E5:84_1"/>
<font color="Maroon" title="c5">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="waybel11.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:84"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c1">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">D</font>,<font color="Maroon" title="c2">R2</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E3:84"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="waybel11.html#E6:84"><i><font color="Green" title="E57">A4</font></i></a>, <a class="ref" href="yellow_0.html#D10" title="YELLOW_0:def.10">YELLOW_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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