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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/>

<b>assume </b><a NAME="E1:74"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:74"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<a NAME="E3:74"/><b>then </b><i><font color="Green">E43</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>thus </b><a NAME="E4:74"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a>  )
 <b>by </b><i><a class="txt" href="tops_3.html#E3:74"><i><font color="Green">E43</font></i></a></i>;<br/>

<b>thus </b><a NAME="E5:74"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a>  implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:74_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a> 
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="txt" href="tops_3.html#E3:74"><i><font color="Green">E43</font></i></a>, <a class="txt" href="tops_3.html#E1:74_1"><i><font color="Green">E44</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="pre_topc.html#T22">PRE_TOPC:22</a></i>
;<br/>


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


</div>
