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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">M</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.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> holds  <font color="Olive" title="b3">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Olive" title="b1">A</font> is   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Olive" title="b2">M</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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> holds  <font color="Olive" title="b1">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> is   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c3">M</font></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> is   <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c3">M</font></span><br/>







<a NAME="E1:57"/>
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M4" title="PBOOLE:mode.4">ManySortedSubset</a> of  <a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>proof </b></a><div class="add">

<a NAME="E1:57_1"/>
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E2:57_1"/><b>then </b><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T59" title="PBOOLE:th.59">PBOOLE:59</a></i>;<br/>
<a NAME="E3:57_1"/>
<span class="p1">(<span class="default"><a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T62" title="PBOOLE:th.62">PBOOLE:62</a></i>;<br/>
<b>hence </b><a NAME="E4:57_1"/>
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K3" title="MSSUBFAM:func.3">bool</a> <font color="Maroon" title="c3">M</font>
 <b>by </b><i><a class="txt" href="#E2:57_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:57"/>
<font color="Maroon" title="c4">SF</font> <a href="pboole.html#K4" title="PBOOLE:func.4">\</a> <font color="Maroon" title="c2">A</font> is   <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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