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<b>let </b><font color="Maroon" title="c1">N</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/>

<b>set </b><font color="Maroon" title="c2">f</font> =  <a href="yellow_2.html#K3" title="YELLOW_2:func.3">IdsMap</a> <font color="Maroon" title="c1">N</font>;<br/>
<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">N</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a><br/>

<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E8">A1</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_2.html#K3" title="YELLOW_2:func.3">IdsMap</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K3" title="YELLOW_2:func.3">IdsMap</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>
 ;<br/>

<a NAME="E2:26"/>
( <span class="p1">(<span class="default"><a href="yellow_2.html#K3" title="YELLOW_2:func.3">IdsMap</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c3">x</font> &amp; <span class="p1">(<span class="default"><a href="yellow_2.html#K3" title="YELLOW_2:func.3">IdsMap</a> <font color="Maroon" title="c1">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c4">y</font> )
 
<b>by </b><i><a class="ref" href="yellow_2.html#D4" title="YELLOW_2:def.4">YELLOW_2:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:26"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="yellow13.html#E1:26"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="waybel_0.html#T19" title="WAYBEL_0:th.19">WAYBEL_0:19</a></i>;<br/>


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