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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">B</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:26"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:26"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" target="_self" title="FUNCOP_1:th.19">Th19</a></span>;<br/>
<a NAME="E3:26"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:26"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T173" title="RELAT_1:th.173">RELAT_1:173</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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