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<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c4">B</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c2">J</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c4">B</font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="altcat_2.html#R2" title="ALTCAT_2:pred.2">cc=</a> <font color="Maroon" title="c3">A</font>
 ;<br/>

<a NAME="E3:14"/><i><font color="Green" title="E6">A3</font></i>: 
( <font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">J</font> &amp; <font color="Maroon" title="c2">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">I</font> )
 
<b>by </b><i><a class="txt" href="altcat_2.html#E1:14"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="altcat_2.html#E2:14"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">B'</font> = <font color="Maroon" title="c4">B</font> as    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_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="E1:14_1"/>
<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/><a NAME="E2:14_1"/><b>then </b>
( <font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> &amp; <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> <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="altcat_2.html#E1:14"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="altcat_2.html#E2:14"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="altcat_2.html#E3:14"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="altcat_2.html#D2" target="_self" title="ALTCAT_2:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:14_1"/>
<font color="Maroon" title="c3">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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B'</font> <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="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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