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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="robbins3.html#L3" target="_self">LattRelStr</a> ;<br/>

<b>assume </b><a NAME="E1:72_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="robbins3.html#V10" target="_self">naturally_sup-generated</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattices.html#V10">Lattice-like</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V10">Lattice-like</a> <a href="robbins3.html#V10" target="_self">naturally_sup-generated</a>  <a href="robbins3.html#L3" target="_self">LattRelStr</a>  ;<br/>
<a NAME="E3:72_1_1"/>
(  <a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>2</sub></font> is <a href="lattice3.html#V1">with_suprema</a> &amp;  <a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">c<sub>2</sub></font> is <a href="lattice3.html#V2">with_infima</a> )
 
;<br/>
<a NAME="E4:72_1_1"/><b>then </b>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) is <a href="lattice3.html#V1">with_suprema</a> &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) is <a href="lattice3.html#V2">with_infima</a> )
 
<b>by </b><i><a class="ref" href="robbins3.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E5:72_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="lattice3.html#V2">with_infima</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="lattice3.html#V1">with_suprema</a> )
 <b>by </b><i><a class="ref" href="yellow_7.html#T15">YELLOW_7:15</a>, <a class="ref" href="yellow_7.html#T14">YELLOW_7:14</a></i>;<br/>


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