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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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">S</font> being  <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>  st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K10" title="EQREL_1:func.10">SmallestPartition</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> holds <br/><font color="Olive" title="b1">S</font> is    <a href="taxonom1.html#M2" title="TAXONOM1:mode.2">Strong_Classification</a> of <font color="Maroon" title="c1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K10" title="EQREL_1:func.10">SmallestPartition</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> implies <font color="Maroon" title="c2">S</font> is    <a href="taxonom1.html#M2" title="TAXONOM1:mode.2">Strong_Classification</a> of <font color="Maroon" title="c1">A</font> )</span><br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K10" title="EQREL_1:func.10">SmallestPartition</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">S</font> is    <a href="taxonom1.html#M2" title="TAXONOM1:mode.2">Strong_Classification</a> of <font color="Maroon" title="c1">A</font></span><br/>

<a NAME="E2:19"/><i><font color="Green" title="E16">A2</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="taxonom1.html#E1:19"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="taxonom1.html#T14" target="_self" title="TAXONOM1:th.14">Th14</a></i>;<br/>
<a NAME="E3:19"/><i><font color="Green" title="E17">A3</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> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="taxonom1.html#E1:19"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E4:19"/>
 <a href="eqrel_1.html#K10" title="EQREL_1:func.10">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="txt" href="taxonom1.html#E1:19"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:19"/>
<font color="Maroon" title="c2">S</font> is    <a href="taxonom1.html#M2" title="TAXONOM1:mode.2">Strong_Classification</a> of <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="taxonom1.html#E2:19"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="taxonom1.html#E3:19"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="taxonom1.html#D2" target="_self" title="TAXONOM1:def.2">Def2</a></i>; <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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