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<b>set </b><font color="Maroon" title="c3">s</font> = <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K7" title="WAYBEL_4:func.7">-below</a> ;<br/>
<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</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="orders_3.html#D5" title="ORDERS_3:def.5">ORDERS_3:def 5</a><br/>

<a NAME="E1:47_1_1"/><i><font color="Green" title="E27">A1</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K7" title="WAYBEL_4:func.7">-below</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K7" title="WAYBEL_4:func.7">-below</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c5">y</font> )
 
<b>by </b><i><a class="ref" href="waybel_4.html#D13" target="_self" title="WAYBEL_4:def.13">Def13</a></i>;<br/>
<b>assume </b><a NAME="E2:47_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">y</font>
 ;<br/>

<a NAME="E3:47_1_1"/><b>then </b>
<font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c5">y</font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#T17" target="_self" title="WAYBEL_4:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E4:47_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K7" title="WAYBEL_4:func.7">-below</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">AR</font> <a href="waybel_4.html#K7" title="WAYBEL_4:func.7">-below</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">y</font> or <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_4.html#E1:47_1_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>


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