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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="membered.html#V1" title="MEMBERED:attr.1">complex-membered</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="membered.html#D13" title="MEMBERED:def.13">MEMBERED:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> ) &amp; (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  ) )</span><br/>





<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:57_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span></span><br/><a NAME="E2:57_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T29" target="_self" title="MEMBER_1:th.29">Th29</a></span>;<br/><a NAME="E3:57_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:57_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T29" target="_self" title="MEMBER_1:th.29">Th29</a></span>;<br/><span class="kw">hence </span><a NAME="E5:57_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:57"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a> </span><br/>

<a NAME="E3:57"/><span class="kw">then </span>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E4:57"/><span class="kw">then </span>
( <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T29" target="_self" title="MEMBER_1:th.29">Th29</a></span>;<br/>
<a NAME="E5:57"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:57"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K7" title="MEMBER_1:func.7">""</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="member_1.html#T29" target="_self" title="MEMBER_1:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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