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

<a NAME="E1:26_1_1"/><i><font color="Green">E33</font></i>: 
 <a href="msualg_2.html#K6">SubSort</a> <font color="Maroon">MA</font> <a href="tarski.html#R1">c=</a>  <a href="closure2.html#K6">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">MA</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:26_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msualg_2.html#K6">SubSort</a> <font color="Maroon">MA</font>
 ;<br/>

<a NAME="E2:26_1_1_1"/><b>then </b>
<font color="Maroon">x</font> is    <a href="pboole.html#M4">ManySortedSubset</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">MA</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D12">MSUALG_2:def 12</a></i>;<br/>
<b>hence </b><a NAME="E3:26_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="closure2.html#K6">Bool</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">MA</font>
 <b>by </b><i><a class="ref" href="closure2.html#D1">CLOSURE2:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">SS</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">MA</font> as    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="struct_0.html#G1">1-sorted</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> #) ;<br/>
<b>reconsider </b><font color="Maroon">SF</font> =  <a href="msualg_2.html#K6">SubSort</a> <font color="Maroon">MA</font> as   <a href="closure2.html#NM1">SubsetFamily</a> of <font color="Maroon">SS</font> <b>by </b><i/>;<br/>
<b>take </b>
 <a href="closure2.html#G1">ClosureStr</a>(# <font color="Maroon">SS</font>,<font color="Maroon">SF</font> #)
;<br/>

<b>thus </b><a NAME="E4:26_1_1"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <a href="closure2.html#G1">ClosureStr</a>(# <font color="Maroon">SS</font>,<font color="Maroon">SF</font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">MA</font> &amp; the <a href="closure2.html#U1">Family</a> of <a href="closure2.html#G1">ClosureStr</a>(# <font color="Maroon">SS</font>,<font color="Maroon">SF</font> #) <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K6">SubSort</a> <font color="Maroon">MA</font> )
 ;<br/>


</div>
