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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:10"/>
<font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:10_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1_1_1"/>
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font> or <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1_1"><b>suppose </b></a><a NAME="E1:10_1_1_1_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:10_1_1_1_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1_2"><b>suppose </b></a><a NAME="E1:10_1_1_1_2"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:10_1_1_1_2"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:10_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:10"/>
<font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font>
 ;<br/>


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