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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>set </b><font color="Maroon">C</font> =  <a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font>;<br/>
<b>set </b><font color="Maroon">G</font> =  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span>;<br/>
<a NAME="E1:63"/><i><font color="Green">E25</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p3">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> <a href="msualg_2.html#K11">/\</a> <font color="Maroon">U1</font></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> <a href="pboole.html#K3">/\</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D17">MSUALG_2:def 17</a></i>;<br/>
<a NAME="E2:63"/>
 <a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font> is    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">U1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:63"/><b>then </b>
 <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span> is  <a href="msualg_1.html#V4">strict</a> <a href="osalg_2.html#NM3">OSSubAlgebra</a> of <font color="Maroon">U1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:63"/><b>then </b>
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> 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 <span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> is   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">S1</font> )
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10">MSUALG_2:def 10</a>, <a class="ref" href="osalg_1.html#T17">OSALG_1:17</a></i>;<br/>
<a NAME="E5:63"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> <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="E6:63"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p3">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> <a href="msualg_2.html#K11">/\</a> <font color="Maroon">U1</font></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="pboole.html#T25">PBOOLE:25</a></i>;<br/>
<b>hence </b><a NAME="E7:63"/>
<span class="p1">(<span class="default"><a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p2">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span></span>)</span> <a href="msualg_2.html#K11">/\</a> <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <span class="p1">(<span class="default"><a href="osalg_2.html#K3" target="_self">OSConstants</a> <font color="Maroon">U0</font></span>)</span>
 <b>by </b><i><a class="ref" href="msualg_2.html#T10">MSUALG_2:10</a></i>;<br/>


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