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

<a NAME="E1:89_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font> <a href="toler_1.html#K1" title="TOLER_1:func.1">|_2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c2">S</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="yellow_0.html#T57" target="_self" title="YELLOW_0:th.57">Th57</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">S</font>
;<br/>

<b>thus </b><a NAME="E3:89_1_1"/>
<font color="Maroon" title="c2">S</font> is <a href="yellow_0.html#V7" title="YELLOW_0:attr.7">infs-inheriting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D18" target="_self" title="YELLOW_0:def.18">YELLOW_0:def 18</a><br/>

<b>thus </b><a NAME="E1:89_1_1_1"/>
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">L</font> implies  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> )
 ;<br/>


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

<b>thus </b><a NAME="E4:89_1_1"/>
<font color="Maroon" title="c2">S</font> is <a href="yellow_0.html#V8" title="YELLOW_0:attr.8">sups-inheriting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D19" target="_self" title="YELLOW_0:def.19">YELLOW_0:def 19</a><br/>

<b>thus </b><a NAME="E1:89_1_1_2"/>
(  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">L</font> implies  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> )
 ;<br/>


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

<b>thus </b><a NAME="E5:89_1_1"/>
( not <font color="Maroon" title="c2">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> )
 ;<br/>


</div>
