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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">A</font>, <font color="Olive" title="b2">M</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b3">SF</font> being  <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Olive" title="b2">M</font>  st <font color="Olive" title="b1">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b3">SF</font> holds <br/><font color="Olive" title="b1">A</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of <font color="Olive" title="b2">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">M</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">SF</font> being  <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c3">M</font>  st <font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b1">SF</font> holds <br/><font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of <font color="Maroon" title="c3">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">SF</font> be   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c3">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c4">SF</font> implies <font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of <font color="Maroon" title="c3">M</font> )</span><br/>







<a NAME="E1:56"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">bool</a> <font color="Maroon" title="c3">M</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/>
<span class="kw">assume </span><a NAME="E2:56"/>
<font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c4">SF</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of <font color="Maroon" title="c3">M</font></span><br/>

<a NAME="E3:56"/><span class="kw">then </span>
<font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">bool</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="pboole.html#T9" title="PBOOLE:th.9">PBOOLE:9</a></span>;<br/>
<a NAME="E4:56"/><span class="kw">then </span>
<font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mboolean.html#T19" title="MBOOLEAN:th.19">MBOOLEAN:19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:56"/>
<font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of <font color="Maroon" title="c3">M</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>; <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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