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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> ;<br/><b>let </b><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be   <a href="pboole.html#NM2" title="PBOOLE:NM.2">ManySortedFunction</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/>





<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a>  <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">doms</a> <font color="Maroon" title="c3">G</font>
 ;<br/>

<a NAME="E2:8"/><i><font color="Green" title="E5">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:8"/><i><font color="Green" title="E6">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">FG</font> = <font color="Maroon" title="c2">F</font> <a href="pboole.html#K12" title="PBOOLE:func.12">**</a> <font color="Maroon" title="c3">G</font> as   <a href="pboole.html#NM2" title="PBOOLE:NM.2">ManySortedFunction</a> of <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="ref" href="mssubfam.html#T15" title="MSSUBFAM:th.15">MSSUBFAM:15</a></i>;<br/>
<a NAME="E5:8"/><i><font color="Green" title="E7">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">FG</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:8"/><i><font color="Green" title="E8">A5</font></i>: 
<font color="Maroon" title="c5">FG</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <font color="Maroon" title="c4">A</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:8_1"/><i><font color="Green" title="E9">A6</font></i>: 
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/><b>reconsider </b><font color="Maroon" title="c8">g</font> = <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/><b>reconsider </b><font color="Maroon" title="c9">fg</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="pboole.html#K12" title="PBOOLE:func.12">**</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/><a NAME="E5:8_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K1" title="MSSUBFAM:func.1">doms</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>by </b><i><a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="mssubfam.html#T14" title="MSSUBFAM:th.14">MSSUBFAM:14</a></i>;<br/><a NAME="E6:8_1"/><b>then </b><i><font color="Green" title="E10">A7</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">g</font>
 <b>by </b><i><a class="txt" href="closure1.html#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="pboole.html#D4" title="PBOOLE:def.4">PBOOLE:def 4</a></i>;<br/><a NAME="E7:8_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="closure1.html#E3:8"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="pralg_1.html#D17" title="PRALG_1:def.17">PRALG_1:def 17</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <font color="Maroon" title="c4">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> = 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="closure1.html#E2:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="pralg_1.html#D17" title="PRALG_1:def.17">PRALG_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="closure1.html#E6:8_1"><i><font color="Green" title="E10">A7</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c9">fg</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>
<b>by </b><i><a class="txt" href="closure1.html#E5:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="pboole.html#D24" title="PBOOLE:def.24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="pboole.html#K12" title="PBOOLE:func.12">**</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="pralg_1.html#K15" title="PRALG_1:func.15">..</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<b>by </b><i><a class="txt" href="closure1.html#E5:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="closure1.html#E1:8_1"><i><font color="Green" title="E9">A6</font></i></a>, <a class="ref" href="pralg_1.html#D17" title="PRALG_1:def.17">PRALG_1:def 17</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:8"/>
<font color="Maroon" title="c2">F</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="pboole.html#K12" title="PBOOLE:func.12">**</a> <font color="Maroon" title="c3">G</font></span>)</span> <a href="pralg_1.html#K15" title="PRALG_1:func.15">..</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="closure1.html#E6:8"><i><font color="Green" title="E8">A5</font></i></a>, <a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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