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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>reconsider </b><font color="Maroon">R</font> = <font color="Maroon">T</font> as  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="yellow_6.html#T15">YELLOW_6:15</a></i>;<br/>
<a NAME="E2:16"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">R</font> is <a href="yellow_0.html#V7">infs-inheriting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D18">YELLOW_0:def 18</a><br/>

<b>thus </b><a NAME="E1:16_1"/>
(  not  <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> or  <a href="yellow_0.html#K2">"/\"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:16"/>
<font color="Maroon">R</font> is <a href="yellow_0.html#V8">sups-inheriting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D19">YELLOW_0:def 19</a><br/>

<b>thus </b><a NAME="E1:16_2"/>
(  not  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> or  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon">T</font> is  <a href="yellow_0.html#V4">full</a> <a href="yellow_0.html#V7">infs-inheriting</a> <a href="yellow_0.html#V8">sups-inheriting</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">T</font>
 <b>by </b><i/>;<br/>


</div>
