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

<b>let </b><font color="Maroon">R1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">R2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:90"/><i><font color="Green">E41</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R1</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R2</font> #)
 ;<br/>

<b>let </b><font color="Maroon">N1</font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R1</font>;<br/><b>let </b><font color="Maroon">N2</font> be   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R2</font>;<br/>



<b>assume </b><a NAME="E2:90"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">N1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N2</font>
 ;<br/>

<b>let </b><font color="Maroon">J1</font> be    <a href="yellow_6.html#M3">net_set</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N1</font>,<font color="Maroon">R1</font>;<br/>

<b>reconsider </b><font color="Maroon">J2</font> = <font color="Maroon">J1</font> as    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N2</font> <b>by </b><i/>;<br/>
<a NAME="E4:90"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">J2</font> holds <br/><font color="Olive">i</font> is   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:90_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">J2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">N</font> = <font color="Maroon">i</font> as   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R1</font> <b>by </b><i><a class="ref" href="yellow_6.html#D15">YELLOW_6:def 15</a></i>;<br/>
<a NAME="E3:90_1"/>
<font color="Maroon">N</font> is    <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">R2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:90_1"/>
<font color="Maroon">i</font> is   <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">R2</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:90"/>
<font color="Maroon">J1</font> is    <a href="yellow_6.html#M3">net_set</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N2</font>,<font color="Maroon">R2</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D15">YELLOW_6:def 15</a></i>;<br/>


</div>
