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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="msualg_1.html#V5">non-empty</a> <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>, <font color="Maroon">c<sub>4</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>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font> 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">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E2:68"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> is   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</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_1.html#T17">OSALG_1:17</a></i>;<br/>
<a NAME="E3:68"/>
( <font color="Maroon">c<sub>5</sub></font> <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> &amp; <font color="Maroon">c<sub>6</sub></font> <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="E4:68"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>6</sub></font> <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#T18">PBOOLE:18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>6</sub></font> 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="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E6:68"/>
<font color="Maroon">c<sub>7</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="txt" href="osalg_2.html#E2:68"><i><font color="Green">E45</font></i></a>, <a class="ref" href="osalg_2.html#T2" target="_self">Th2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="osalg_2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E8:68"/>
<font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="osalg_2.html#K10" target="_self">GenOSAlg</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="osalg_2.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E9:68"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is    <a href="osalg_2.html#M2" target="_self">OSSubset</a> of <font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</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="E10:68"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>8</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"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E11:68"/>
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> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16">PBOOLE:16</a></i>;<br/>
<a NAME="E12:68"/><b>then </b><i><font color="Green">E47</font></i>: 
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"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E10:68"><i><font color="Green">E46</font></i></a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<a NAME="E13:68"/><i><font color="Green">E48</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></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">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D17">MSUALG_2:def 17</a></i>;<br/>
<a NAME="E14:68"/><b>then </b><i><font color="Green">E49</font></i>: 
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"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E12:68"><i><font color="Green">E47</font></i></a>, <a class="ref" href="pboole.html#T19">PBOOLE:19</a></i>;<br/>
<a NAME="E15:68"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E13:68"><i><font color="Green">E48</font></i></a>, <a class="ref" href="pboole.html#T17">PBOOLE:17</a></i>;<br/>
<a NAME="E16:68"/><b>then </b><i><font color="Green">E50</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="osalg_2.html#E14:68"><i><font color="Green">E49</font></i></a>, <a class="ref" href="pboole.html#D13">PBOOLE:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></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">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E18:68"/>
( <font color="Maroon">c<sub>9</sub></font> is <a href="msualg_2.html#V3">opers_closed</a> &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pboole.html#R6">=</a>  <a href="msualg_2.html#K4">Opers</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="msualg_2.html#D17">MSUALG_2:def 17</a></i>;<br/>
<b>hence </b><a NAME="E19:68"/>
<font color="Maroon">c<sub>3</sub></font> <a href="msualg_2.html#K11">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="osalg_2.html#K11" target="_self">"\/"_os</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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#E16:68"><i><font color="Green">E50</font></i></a>, <a class="ref" href="msualg_2.html#D10">MSUALG_2:def 10</a></i>;<br/>


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