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

<b>let </b><font color="Maroon" title="c1">S1</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon" title="c2">U0</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Maroon" title="c1">S1</font>;<br/><b>let </b><font color="Maroon" title="c3">U1</font> be   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <font color="Maroon" title="c2">U0</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font>;<br/>







<a NAME="E1:64"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c4">A</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c5">B</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> )
 
<b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<b>assume </b><a NAME="E2:64"/><i><font color="Green" title="E42">A2</font></i>: 
<font color="Maroon" title="c5">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">U1</font>
 ;<br/>

<a NAME="E3:64"/>
<font color="Maroon" title="c4">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E4:64"/><b>then </b><i><font color="Green" title="E43">A3</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">u1m</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">U1</font>, <font color="Maroon" title="c7">am</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green" title="E44">A4</font></i>: 
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">U1</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font> )
 
<b>by </b><i><a class="ref" href="osalg_1.html#T17" title="OSALG_1:th.17">OSALG_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">u1</font> = <font color="Maroon" title="c6">u1m</font>, <font color="Maroon" title="c9">a</font> = <font color="Maroon" title="c7">am</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E8:64"/>
( <font color="Maroon" title="c9">a</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U0</font> &amp; <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U0</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E9:64"/><b>then </b>
<font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U0</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E11:64"/><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S1</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E6:64"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="osalg_2.html#T2" target="_self" title="OSALG_2:th.2">Th2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">b</font> = <font color="Maroon" title="c10">b</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font> <b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E13:64"/><i><font color="Green" title="E46">A6</font></i>: 
<span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c11">b</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D14" target="_self" title="OSALG_2:def.14">Def14</a></i>;<br/>
<a NAME="E14:64"/><b>then </b>
<font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E15:64"/><b>then </b><i><font color="Green" title="E47">A7</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E16:64"/>
<font color="Maroon" title="c4">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c9">a</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c8">u1</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:64"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="pboole.html#T22" title="PBOOLE:th.22">PBOOLE:22</a></i>;<br/>
<a NAME="E17:64"/><b>then </b>
<font color="Maroon" title="c5">B</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E2:64"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="osalg_2.html#E15:64"><i><font color="Green" title="E47">A7</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E18:64"/><b>then </b>
<font color="Maroon" title="c5">B</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E19:64"/><b>then </b>
<font color="Maroon" title="c5">B</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E1:64"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E20:64"/><b>then </b><i><font color="Green" title="E48">A8</font></i>: 
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E21:64"/>
( <font color="Maroon" title="c5">B</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font> )
 
<b>by </b><i><a class="txt" href="osalg_2.html#E2:64"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a>, <a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E22:64"/><b>then </b>
( <font color="Maroon" title="c5">B</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span> &amp; <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">B</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E23:64"/><b>then </b><i><font color="Green" title="E49">A9</font></i>: 
( <font color="Maroon" title="c8">u1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span> &amp; <font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<a NAME="E24:64"/><b>then </b><i><font color="Green" title="E50">A10</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:64"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="pboole.html#T19" title="PBOOLE:th.19">PBOOLE:19</a></i>;<br/>
<a NAME="E25:64"/><i><font color="Green" title="E51">A11</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D17" title="MSUALG_2:def.17">MSUALG_2:def 17</a></i>;<br/>
<a NAME="E26:64"/><b>then </b>
<font color="Maroon" title="c4">A</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E24:64"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E27:64"/><b>then </b>
<font color="Maroon" title="c4">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E1:64"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E28:64"/><b>then </b>
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font> is   <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E29:64"/><b>then </b>
<font color="Maroon" title="c9">a</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="msualg_2.html#K11" title="MSUALG_2:func.11">/\</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E30:64"/><b>then </b><i><font color="Green" title="E52">A12</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E25:64"><i><font color="Green" title="E51">A11</font></i></a>, <a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E31:64"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c9">a</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T17" title="PBOOLE:th.17">PBOOLE:17</a></i>;<br/>
<a NAME="E32:64"/><b>then </b>
<font color="Maroon" title="c9">a</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E30:64"><i><font color="Green" title="E52">A12</font></i></a>, <a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a></i>;<br/>
<a NAME="E33:64"/><b>then </b>
<font color="Maroon" title="c9">a</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T17" title="PBOOLE:th.17">PBOOLE:17</a></i>;<br/>
<a NAME="E34:64"/><b>then </b>
<font color="Maroon" title="c11">b</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E23:64"><i><font color="Green" title="E49">A9</font></i></a>, <a class="ref" href="pboole.html#T18" title="PBOOLE:th.18">PBOOLE:18</a></i>;<br/>
<a NAME="E35:64"/><b>then </b>
<font color="Maroon" title="c11">b</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E36:64"/><b>then </b>
<font color="Maroon" title="c11">b</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E11:64"><i><font color="Green" title="E45">A5</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<a NAME="E37:64"/><b>then </b>
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c11">b</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a> <a href="osalg_2.html#NM3" title="OSALG_2:NM.3">OSSubAlgebra</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E38:64"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="osalg_2.html#K11" title="OSALG_2:func.11">"\/"_os</a> <font color="Maroon" title="c3">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="txt" href="osalg_2.html#E13:64"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="osalg_2.html#E20:64"><i><font color="Green" title="E48">A8</font></i></a>, <a class="ref" href="msualg_2.html#T8" title="MSUALG_2:th.8">MSUALG_2:8</a></i>;<br/>


</div>
