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

<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E2:1_1_1"/><i><font color="Green">E1</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#T17">OSALG_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="osalg_2.html#M2">OSSubset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="osalg_2.html#D2">OSALG_2:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<a NAME="E4:1_1_1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R6">=</a>  <a href="osalg_2.html#K2">OSCl</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="osafree.html#E2:1_1_1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="osalg_2.html#T14">OSALG_2:14</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="osalg_2.html#K10">GenOSAlg</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E5:1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="osalg_2.html#M2">OSSubset</a> of  <a href="osalg_2.html#K10">GenOSAlg</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13">OSALG_2:def 13</a></i>;<br/>
<a NAME="E6:1_1_1"/><b>then </b><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10">GenOSAlg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E7:1_1_1"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10">GenOSAlg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E8:1_1_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10">GenOSAlg</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<b>hence </b><a NAME="E9:1_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="osalg_2.html#M2">OSSubset</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R6">=</a>  <a href="osalg_2.html#K2">OSCl</a> <font color="Maroon">c<sub>5</sub></font> holds <br/>the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10">GenOSAlg</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="osafree.html#E4:1_1_1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="osafree.html#E6:1_1_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="pboole.html#D13">PBOOLE:def 13</a></i>;<br/>


</div>
