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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V2">upper-bounded</a> <a href="orders_2.html#NM1">Poset</a>;<br/>

<b>assume </b><a NAME="E1:27"/>
 <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font> <a href="hidden.html#R2">in</a>  <a href="waybel16.html#K1" target="_self">Irr</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
 <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font> is <a href="waybel16.html#V1" target="_self">completely-irreducible</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:27"/><b>then </b>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<font color="Maroon">L</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:27"/><b>then </b>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<font color="Maroon">L</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#T24">WAYBEL_4:24</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
 <a href="yellow_0.html#K2">"/\"</a> <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">L</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/>
<b>hence </b><a NAME="E6:27"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow_0.html#D12">YELLOW_0:def 12</a></i>;<br/>


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