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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</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>;<br/>

<b>consider </b><font color="Maroon" title="c3">S'</font> being  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">S</font>;<br/>
<b>consider </b><font color="Maroon" title="c4">T'</font> being  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c2">T</font>;<br/>
<a NAME="E3:43"/><i><font color="Green" title="E29">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">S</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</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="c3">S'</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">S'</font> #) &amp;  <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">T</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</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="c4">T'</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">T'</font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>then </b><i><font color="Green" title="E30">A2</font></i>:  <a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> = 
 <a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c3">S'</font>,<font color="Maroon" title="c4">T'</font>
<b>by </b><i><a class="ref" href="waybel27.html#T25" target="_self" title="WAYBEL27:th.25">Th25</a></i>
<br/>.= 
 <a href="waybel17.html#K2" title="WAYBEL17:func.2">SCMaps</a> <font color="Maroon" title="c3">S'</font>,<font color="Maroon" title="c4">T'</font>
<b>by </b><i><a class="ref" href="waybel27.html#T24" target="_self" title="WAYBEL27:th.24">Th24</a></i>
<br/>.= 
 <a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c3">S'</font>,<font color="Maroon" title="c4">T'</font>
<b>by </b><i><a class="ref" href="waybel24.html#T38" title="WAYBEL24:th.38">WAYBEL24:38</a></i>
;<br/>
<a NAME="E5:43"/>
<font color="Maroon" title="c4">T'</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="txt" href="waybel27.html#E3:43"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="waybel27.html#T15" target="_self" title="WAYBEL27:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E6:43"/>
 <a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> is  <a href="yellow_0.html#V8" title="YELLOW_0:attr.8">sups-inheriting</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">T</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="txt" href="waybel27.html#E3:43"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="waybel27.html#E4:43"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="waybel24.html#T35" title="WAYBEL24:th.35">WAYBEL24:35</a></i>;<br/>


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