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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="msualg_1.html#V4">strict</a> <a href="osalg_2.html#NM3">OSSubAlgebra</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<a NAME="E1:62"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self">Def2</a></i>;<br/>
<b>assume </b><a NAME="E2:62"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E3:62"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:62"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E1:62"><i><font color="Green">E39</font></i></a>, <a class="ref" href="osalg_2.html#D2" target="_self">Def2</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E5:62"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E6:62"/><i><font color="Green">E43</font></i>: 
 <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>4</sub></font> is  <a href="msualg_1.html#V4">strict</a> <a href="osalg_2.html#NM3">OSSubAlgebra</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E4:62"><i><font color="Green">E41</font></i></a>, <a class="ref" href="osalg_2.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E7:62"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</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> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E2:62"><i><font color="Green">E40</font></i></a>, <a class="txt" href="osalg_2.html#E5:62"><i><font color="Green">E42</font></i></a>, <a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E8:62"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1">MSSubAlgebra</a> of  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#T9">MSUALG_2:9</a></i>;<br/>
<b>hence </b><a NAME="E9:62"/>
 <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="osalg_2.html#E6:62"><i><font color="Green">E43</font></i></a>, <a class="ref" href="msualg_2.html#T8">MSUALG_2:8</a></i>;<br/>


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