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

<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">U0</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">U1</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">U2</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:25"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">U0</font> is    <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U1</font> &amp; <font color="Maroon">U1</font> is    <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U2</font> )
 ;<br/>

<a NAME="E2:25"/><b>then </b>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U1</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:25"/><b>then </b><i><font color="Green">E21</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U2</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:25"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U2</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U2</font>
 <b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_2.html#D10" target="_self">MSUALG_2:def 10</a><br/>

<b>let </b><font color="Maroon">B</font> be   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U2</font>;<br/>

<b>assume </b><a NAME="E6:25"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">B</font> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">B0</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U1</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">B1</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U2</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">B1'</font> = <font color="Maroon">B1</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U1</font> <b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E10:25"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">B0</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U0</font> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U1</font>,<font color="Maroon">B0</font> &amp; <font color="Maroon">B1</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U1</font> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B1</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:25"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">o</font> being  <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> holds  <font color="Maroon">B</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Olive">o</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/>

<a NAME="E1:25_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">B0</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font> &amp; <font color="Maroon">B1</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font> )
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E29</font></i>:  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U1</font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
<font color="Maroon">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">B1</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="txt" href="msualg_2.html#E1:25"><i><font color="Green">E20</font></i></a>, </i>
;<br/>
<a NAME="E3:25_1"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1'</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U0</font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U1</font>,<font color="Maroon">B0</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
<font color="Maroon">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">B0</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="txt" href="msualg_2.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="msualg_2.html#E3:25"><i><font color="Green">E21</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="txt" href="msualg_2.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E5:25_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="msualg_1.html#K4">Result</a> <font color="Maroon">o</font>,<font color="Maroon">U0</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:25_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>;<br/>
<b>hence </b><a NAME="E7:25_1"/>
<font color="Maroon">B</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E12:25"/>
<font color="Maroon">B</font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a>
 <b>by </b><i/>;<br/>

<b>set </b><font color="Maroon">O</font> = the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U0</font>;<br/>
<b>set </b><font color="Maroon">P</font> =  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B</font>;<br/>
<a NAME="E13:25"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> holds <br/>the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:25_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">o</font> = <font color="Maroon">x</font> as   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E3:25_2"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">B0</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font> &amp; <font color="Maroon">B1</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font> )
 
<b>by </b><i>, </i>;<br/>
<i><font color="Green">E32</font></i>:  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U1</font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
<font color="Maroon">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">B1</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="txt" href="msualg_2.html#E1:25"><i><font color="Green">E20</font></i></a>, </i>
;<br/>
<a NAME="E5:25_2"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1'</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:25_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">B</font> <a href="msualg_2.html#R1" target="_self">is_closed_on</a> <font color="Maroon">o</font>
 
<b>by </b><i/>;<br/>
<b>thus </b>the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">B0</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="txt" href="msualg_2.html#E1:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="msualg_2.html#E3:25"><i><font color="Green">E21</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B0</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">U2</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i>, <a class="txt" href="msualg_2.html#E6:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
<br/>.= 
<font color="Maroon">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">B</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E14:25"/>
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">U0</font> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U2</font>,<font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div>
