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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="waybel_0.html#NM5">Chain</a>;<br/>

<b>assume </b><a NAME="E1:23_1_1"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="yellow_0.html#V1">lower-bounded</a> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:23_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><b>hence </b><a NAME="E2:23_1_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel_3.html#E1:23_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a>, <a class="ref" href="yellow_0.html#T42">YELLOW_0:42</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:23_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="lattice3.html#V3">complete</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#T53">YELLOW_0:53</a></i>;<br/>


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