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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">x</font>, <font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</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="E1:18"/><i><font color="Green" title="E4">A1</font></i>: 
<span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1"><a href="pzfmisc1.html#K2" title="PZFMISC1:func.2">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="pzfmisc1.html#K2" title="PZFMISC1:func.2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:18_1"/><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ;<br/><b>then </b><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
<span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="ref" href="pzfmisc1.html#D1" target="_self" title="PZFMISC1:def.1">Def1</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="txt" href="pzfmisc1.html#E1:18"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="pzfmisc1.html#E1:18_1"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="pzfmisc1.html#D2" target="_self" title="PZFMISC1:def.2">Def2</a></i>
;<br/><b>hence </b><a NAME="E3:18_1"/>
<font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">i</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T9" title="ZFMISC_1:th.9">ZFMISC_1:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:18"/>
<font color="Maroon" title="c3">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</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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