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<b>let </b><font color="Maroon" title="c1">L1</font> be   <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">L2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>;<br/><b>let </b><font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c6">y1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>;<br/>







<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E9">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">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</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">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font> )
 ;<br/>

<a NAME="E2:13"/><i><font color="Green" title="E10">A2</font></i>: 
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L1</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20" title="YELLOW_0:th.20">YELLOW_0:20</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green" title="E11">A3</font></i>: 
<font color="Maroon" title="c2">L2</font> is  <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>
 
<b>by </b><i><a class="txt" href="yellow12.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="waybel_8.html#T12" title="WAYBEL_8:th.12">WAYBEL_8:12</a>, <a class="ref" href="waybel_8.html#T13" title="WAYBEL_8:th.13">WAYBEL_8:13</a>, <a class="ref" href="waybel_8.html#T14" title="WAYBEL_8:th.14">WAYBEL_8:14</a>, <a class="ref" href="yellow_7.html#T15" title="YELLOW_7:th.15">YELLOW_7:15</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">y</font> = 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
<b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x1</font>,<font color="Maroon" title="c6">y1</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
<b>by </b><i><a class="txt" href="yellow12.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="yellow12.html#E2:13"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="yellow_0.html#T26" title="YELLOW_0:th.26">YELLOW_0:26</a></i>
<br/>.= 
<font color="Maroon" title="c5">x1</font> <a href="lattice3.html#K10" title="LATTICE3:func.10">"\/"</a> <font color="Maroon" title="c6">y1</font>
<b>by </b><i><a class="txt" href="yellow12.html#E3:13"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>
;<br/>


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