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<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">OU0</font> be   <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">OU1</font> be  <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 <font color="Maroon" title="c2">OU0</font>;<br/><b>let </b><font color="Maroon" title="c4">B</font> be    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font>;<br/>







<a NAME="E1:62"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c4">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="E2:62"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c4">B</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 <font color="Maroon" title="c3">OU1</font>
 ;<br/>

<a NAME="E3:62"/><b>then </b>
<font color="Maroon" title="c4">B</font> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c3">OU1</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:62"/><b>then </b><i><font color="Green" title="E41">A3</font></i>: 
<font color="Maroon" title="c4">B</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c3">OU1</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E1:62"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self" title="OSALG_2:def.2">Def2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">W</font> =  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">B</font>;<br/>
<a NAME="E5:62"/><i><font color="Green" title="E42">A4</font></i>: 
<font color="Maroon" title="c4">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="c4">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/>
<a NAME="E6:62"/><i><font color="Green" title="E43">A5</font></i>: 
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">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 <font color="Maroon" title="c3">OU1</font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:62"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="osalg_2.html#D13" target="_self" title="OSALG_2:def.13">Def13</a></i>;<br/>
<a NAME="E7:62"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">OU1</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">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E2:62"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="osalg_2.html#E5:62"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E8:62"/><b>then </b>
<font color="Maroon" title="c3">OU1</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">strict</a>  <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#T9" title="MSUALG_2:th.9">MSUALG_2:9</a></i>;<br/>
<b>hence </b><a NAME="E9:62"/>
 <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">OU1</font>
 <b>by </b><i><a class="txt" href="osalg_2.html#E6:62"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="msualg_2.html#T8" title="MSUALG_2:th.8">MSUALG_2:8</a></i>;<br/>


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