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



<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ;<br/>

<b>thus </b><a NAME="E2:27"/>
<font color="Maroon" title="c2">A</font> <a href="yellow_4.html#R3" title="YELLOW_4:pred.3">is_finer_than</a> <font color="Maroon" title="c3">B</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">a</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="yellow_4.html#D1" title="YELLOW_4:def.1">YELLOW_4:def 1</a><br/>

<b>assume </b><a NAME="E1:27_1"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>take </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">a</font>;<br/>

<b>thus </b><a NAME="E2:27_1"/>
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c4">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">b</font> )
 <b>by </b><i><a class="txt" href="waybel12.html#E1:27"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="waybel12.html#E1:27_1"><i><font color="Green" title="E14">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">a</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="yellow_4.html#D2" title="YELLOW_4:def.2">YELLOW_4:def 2</a><br/>

<b>assume </b><a NAME="E3:27"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>take </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">a</font>;<br/>

<b>thus </b><a NAME="E4:27"/>
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c5">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">a</font> )
 <b>by </b><i><a class="txt" href="waybel12.html#E1:27"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="waybel12.html#E3:27"><i><font color="Green" title="E14">A3</font></i></a></i>;<br/>


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