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<b>let </b><font color="Maroon">S1</font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">U0</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">U1</font> be   <a href="osalg_2.html#NM3">OSSubAlgebra</a> of <font color="Maroon">U0</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">U0</font>;<br/>







<b>assume </b><a NAME="E1:66"/><i><font color="Green">E25</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/>

<a NAME="E2:66"/>
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">U0</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E3:66"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#T5" target="_self">Th5</a>, <a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:66"/><b>then </b>
<font color="Maroon">B</font> <a href="pboole.html#K2">\/</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T24">PBOOLE:24</a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">B</font></span>)</span> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="osalg_2.html#T4" target="_self">Th4</a></i>;<br/>


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