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<b>let </b><font color="Maroon" title="c3">S</font>, <font color="Maroon" title="c4">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c4">T</font> implies <font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c3">S</font> )</span><br/>

<b>assume </b><a NAME="E1:18_1_2"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c4">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c3">S</font></span><br/>

<a NAME="E2:18_1_2"/>
<font color="Maroon" title="c4">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">E</font>
 
<b>by </b><i><a class="ref" href="subset_1.html#D2" target="_self" title="SUBSET_1:def.2">Def2</a></i>;<br/>
<a NAME="E3:18_1_2"/><b>then </b>
<font color="Maroon" title="c4">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">E</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1" title="ZFMISC_1:def.1">ZFMISC_1:def 1</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c4">T</font> = 
<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">T</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">T</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>
<br/>.= 
<font color="Maroon" title="c1">E</font> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <font color="Maroon" title="c3">S</font>
<b>by </b><i><a class="txt" href="#E1:18_1_2"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="xboole_1.html#T52" title="XBOOLE_1:th.52">XBOOLE_1:52</a></i>
;<br/> <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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