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<a NAME="E1:18_1_1"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T48" title="EQREL_1:th.48">EQREL_1:48</a></i>;<br/>
<a NAME="E2:18_1_1"/><b>then </b><i><font color="Green" title="E14">A1</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K1" title="PARTIT1:func.1">PARTITIONS</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D3" title="PARTIT1:def.3">PARTIT1:def 3</a></i>;<br/>
<a NAME="E3:18_1_1"/>
 <a href="eqrel_1.html#K11" title="EQREL_1:func.11">SmallestPartition</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K1" title="PARTIT1:func.1">PARTITIONS</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D3" title="PARTIT1:def.3">PARTIT1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c2">S</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2">(<span class="default"><a href="eqrel_1.html#K11" title="EQREL_1:func.11">SmallestPartition</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="partit1.html#K1" title="PARTIT1:func.1">PARTITIONS</a> <font color="Maroon" title="c1">A</font></span>)</span> <b>by </b><i><a class="txt" href="taxonom1.html#E2:18_1_1"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">S</font>
;<br/>

<b>thus </b><a NAME="E5:18_1_1"/>
( <font color="Maroon" title="c2">S</font> is    <a href="taxonom1.html#M1" title="TAXONOM1:mode.1">Classification</a> of <font color="Maroon" title="c1">A</font> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> &amp;  <a href="eqrel_1.html#K11" title="EQREL_1:func.11">SmallestPartition</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> )
 <b>by </b><i><a class="ref" href="taxonom1.html#T14" target="_self" title="TAXONOM1:th.14">Th14</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>


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