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<b>let </b><font color="Maroon">S</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">U0</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">U1</font> be  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U0</font>, <font color="Maroon">U2</font> be  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">U0</font>;<br/>





<b>reconsider </b><font color="Maroon">u1</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font>, <font color="Maroon">u2</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U2</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/>
<a NAME="E2:59"/>
( <font color="Maroon">u1</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> &amp; <font color="Maroon">u2</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E3:59"/><b>then </b>
<font color="Maroon">u1</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">u2</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18">PBOOLE:18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">u1</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">u2</font> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> <b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E5:59"/>
<font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font> <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:59"/><b>then </b>
<font color="Maroon">A</font> is   <a href="msualg_2.html#NM1">MSSubset</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:59"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">A</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E8:59"/>
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">A</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16">PBOOLE:16</a></i>;<br/>
<a NAME="E9:59"/><b>then </b><i><font color="Green">E21</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D2" target="_self">Def2</a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<a NAME="E10:59"/><i><font color="Green">E22</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#K3">/\</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E11:59"/><b>then </b><i><font color="Green">E26</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U1</font> <a href="pboole.html#R2">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D3" target="_self">Def3</a>, <a class="ref" href="pboole.html#T19">PBOOLE:19</a></i>;<br/>
<a NAME="E12:59"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</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#T17">PBOOLE:17</a></i>;<br/>
<a NAME="E13:59"/><b>then </b><i><font color="Green">E27</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span></span>)</span> <a href="pboole.html#R6">=</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#D13">PBOOLE:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">u112</font> = the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span></span>)</span> as   <a href="msualg_2.html#NM1">MSSubset</a> of <font color="Maroon">U0</font> <b>by </b><i/>;<br/>
<a NAME="E15:59"/>
( <font color="Maroon">u112</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"><font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">u112</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E16:59"/>
<font color="Maroon">U1</font> <a href="msualg_2.html#K11" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">U1</font> <a href="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">U2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">U1</font>
 <b>by </b><i>, </i>;<br/>


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