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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_1.html#L3">MSAlgebra</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_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:52"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:52"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> is   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E3:52"/><b>then </b><i><font color="Green">E37</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E4:52"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msualg_2.html#E1:52"><i><font color="Green">E36</font></i></a>, <a class="ref" href="msualg_2.html#D18" target="_self">Def18</a></i>;<br/>
<a NAME="E5:52"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</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="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E6:52"/><b>then </b><i><font color="Green">E38</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msualg_2.html#E3:52"><i><font color="Green">E37</font></i></a>, <a class="ref" href="pboole.html#D13">PBOOLE:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="msualg_2.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E8:52"/>
( <font color="Maroon">c<sub>5</sub></font> is <a href="msualg_2.html#V3" target="_self">opers_closed</a> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E9:52"/>
 <a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="msualg_2.html#E6:52"><i><font color="Green">E38</font></i></a>, <a class="ref" href="msualg_2.html#T5" target="_self">Th5</a></i>;<br/>


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