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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="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E44">A1</font></i>: 
for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b1">D1</font></span>)</span> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b2">D2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">D1</font> <a href="yellow_4.html#K3" title="YELLOW_4:func.3">"/\"</a> <font color="Olive" title="b2">D2</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D6" target="_self" title="WAYBEL_2:def.6">WAYBEL_2:def 6</a><br/><b>let </b><font color="Maroon" title="c3">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<a NAME="E2:67"/><i><font color="Green" title="E45">A2</font></i>: 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T5" title="WAYBEL_0:th.5">WAYBEL_0:5</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">D</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">D</font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_0.html#T39" title="YELLOW_0:th.39">YELLOW_0:39</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="yellow_4.html#K3" title="YELLOW_4:func.3">"/\"</a> <font color="Maroon" title="c3">D</font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_2.html#E1:67"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="waybel_2.html#E2:67"><i><font color="Green" title="E45">A2</font></i></a></i>
;<br/>


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