<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">transitive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">J</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">N</font>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="yellow_4.html#R2" title="YELLOW_4:pred.2">is_coarser_than</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c3">J</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">w</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:34"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">w1</font> = <font color="Maroon" title="c4">w</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">N</font> ;<br/>
<b>consider </b><font color="Maroon" title="c6">t</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">N</font><b> such that </b><br/><a NAME="E5:34"/><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c6">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">w1</font> &amp; <font color="Maroon" title="c6">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="txt" href="yellow12.html#E2:34"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="waybel_0.html#D16" title="WAYBEL_0:def.16">WAYBEL_0:def 16</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">t1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">N</font><b> such that </b><br/><a NAME="E7:34"/><i><font color="Green" title="E16">A4</font></i>: 
( <font color="Maroon" title="c7">t1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Maroon" title="c7">t1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">t</font> )
 <b>by </b><i><a class="txt" href="yellow12.html#E1:34"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="yellow12.html#E5:34"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="yellow_4.html#D2" title="YELLOW_4:def.2">YELLOW_4:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">t2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">N</font><b> such that </b><br/><a NAME="E9:34"/><i><font color="Green" title="E17">A5</font></i>: 
( <font color="Maroon" title="c8">t2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">t1</font> &amp; <font color="Maroon" title="c8">t2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> )
 <b>by </b><i><a class="txt" href="yellow12.html#E7:34"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="waybel_0.html#D16" title="WAYBEL_0:def.16">WAYBEL_0:def 16</a></i>;<br/>
<a NAME="E10:34"/>
<font color="Maroon" title="c8">t2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">t</font>
 
<b>by </b><i><a class="txt" href="yellow12.html#E7:34"><i><font color="Green" title="E16">A4</font></i></a>, <a class="txt" href="yellow12.html#E9:34"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/>
<a NAME="E11:34"/><b>then </b>
<font color="Maroon" title="c8">t2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">w1</font>
 
<b>by </b><i><a class="txt" href="yellow12.html#E5:34"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/>
<b>hence </b><a NAME="E12:34"/>
<font color="Maroon" title="c4">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c3">J</font>
 <b>by </b><i><a class="txt" href="yellow12.html#E9:34"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="waybel_0.html#D16" title="WAYBEL_0:def.16">WAYBEL_0:def 16</a></i>;<br/>


</div>
