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<span class="kw">set </span><font color="Maroon" title="c3">A</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">A</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E2:1_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
<font color="Maroon" title="c4">A</font> is   <a href="osalg_1.html#NM4" title="OSALG_1:NM.4">OrderSortedSet</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T17" title="OSALG_1:th.17">OSALG_1:17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">A</font> = <font color="Maroon" title="c4">A</font> as    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D2" title="OSALG_2:def.2">OSALG_2:def 2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">A</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">O</font> being   <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font>  st <font color="Olive" title="b1">O</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <font color="Maroon" title="c5">A</font> holds <br/>the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b1">O</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">G</font> =  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">A</font>;<br/>
<a NAME="E4:1_1_1"/>
<font color="Maroon" title="c5">A</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of  <a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D13" title="OSALG_2:def.13">OSALG_2:def 13</a></span>;<br/>
<a NAME="E5:1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<font color="Maroon" title="c5">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E6:1_1_1"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">A</font></span>)</span> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></span>;<br/>
<a NAME="E7:1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E3">A3</font></span>: 
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Maroon" title="c5">A</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<a NAME="E8:1_1_1"/>
<font color="Maroon" title="c5">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <font color="Maroon" title="c5">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="osalg_2.html#T14" title="OSALG_2:th.14">OSALG_2:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:1_1_1"/>
for <font color="Olive" title="b1">O</font> being   <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">U0</font>  st <font color="Olive" title="b1">O</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="osalg_2.html#K2" title="OSALG_2:func.2">OSCl</a> <font color="Maroon" title="c5">A</font> holds <br/>the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="osalg_2.html#K10" title="OSALG_2:func.10">GenOSAlg</a> <font color="Olive" title="b1">O</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E7:1_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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