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<b>let </b><font color="Maroon">T</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">S</font> is <a href="yellow_0.html#V8">sups-inheriting</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>set </b><font color="Maroon">Y</font> = <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>;<br/><b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><a NAME="E2:23_1"/><i><font color="Green">E30</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">Y</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/><a NAME="E3:23_1"/><b>then </b>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">Y</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#D19">YELLOW_0:def 19</a></i>;<br/><a NAME="E4:23_1"/><b>then </b>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">Y</font>,<font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T65">YELLOW_0:65</a></i>;<br/><b>hence </b><a NAME="E5:23_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T50">YELLOW_0:50</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:23"/>
<font color="Maroon">S</font> is <a href="lattice3.html#V3">complete</a>
 <b>by </b><i><a class="ref" href="yellow_2.html#T26">YELLOW_2:26</a></i>;<br/>


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