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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="robbins3.html#L3" title="ROBBINS3:struct.3">LattRelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V10" title="ROBBINS3:attr.10">naturally_sup-generated</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> implies ( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> ) )</span><br/>

<b>assume </b><a NAME="E1:72_1_1"/>
( <font color="Maroon" title="c1">L</font> is <a href="robbins3.html#V10" title="ROBBINS3:attr.10">naturally_sup-generated</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> )</span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">L'</font> = <font color="Maroon" title="c1">L</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> <a href="robbins3.html#V10" title="ROBBINS3:attr.10">naturally_sup-generated</a>  <a href="robbins3.html#L3" title="ROBBINS3:struct.3">LattRelStr</a>  ;<br/>
<a NAME="E3:72_1_1"/>
(  <a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c2">L'</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> &amp;  <a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c2">L'</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> )
 
;<br/>
<a NAME="E4:72_1_1"/><b>then </b>
(  <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">L'</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L'</font> #) is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> &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">L'</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L'</font> #) is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> )
 
<b>by </b><i><a class="ref" href="robbins3.html#T23" target="_self" title="ROBBINS3:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E5:72_1_1"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> )
 <b>by </b><i><a class="ref" href="yellow_7.html#T14" title="YELLOW_7:th.14">YELLOW_7:14</a>, <a class="ref" href="yellow_7.html#T15" title="YELLOW_7:th.15">YELLOW_7:15</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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