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<b>let </b><font color="Maroon">H</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:113"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">H</font> is   <a href="waybel_0.html#NM8">LATTICE</a> &amp; ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> holds  <font color="Olive">x</font> <a href="waybel_1.html#K4" target="_self">"/\"</a>  <a href="waybel_1.html#NR9" target="_self">has_an_upper_adjoint</a>  ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D19" target="_self">WAYBEL_1:def 19</a><br/>

<a NAME="E2:113"/><b>then </b>
for <font color="Olive">X</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">H</font>  st  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Olive">X</font>,<font color="Maroon">H</font> holds <br/>for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> holds  <font color="Olive">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <font color="Olive">X</font>,<font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font></span>)</span> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> : <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">X</font> </span>}</span> ,<font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:113"/>
<font color="Maroon">H</font> is <a href="waybel_1.html#V2" target="_self">distributive</a>
 <b>by </b><i>, </i>;<br/>


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