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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#V5">non-empty</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="E1:73"/><i><font color="Green">E53</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#K17" target="_self">MSSubAlLattice</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="msualg_2.html#D20" target="_self">Def20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K17" target="_self">MSSubAlLattice</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_2.html#K17" target="_self">MSSubAlLattice</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_2.html#K14" target="_self">MSSub</a> <font color="Maroon">c<sub>2</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as  <a href="msualg_1.html#V4">strict</a>  <a href="msualg_2.html#M1" target="_self">MSSubAlgebra</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="msualg_2.html#D20" target="_self">Def20</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="msualg_2.html#K15" target="_self">MSAlg_join</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>

<br/>.= 
<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="msualg_2.html#K13" target="_self">"\/"</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="msualg_2.html#D21" target="_self">Def21</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="msualg_2.html#E1:73"><i><font color="Green">E53</font></i></a>, <a class="ref" href="msualg_2.html#T26" target="_self">Th26</a></i>
;<br/><b>hence </b><a NAME="E4:73_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:73"/>
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K17" target="_self">MSSubAlLattice</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K12" target="_self">GenMSAlg</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/>


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