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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c4">D</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"> ( <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> implies <font color="Maroon" title="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c4">D</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:153"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
( <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D</font> )
 ; <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="c1">A</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="member_1.html#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c4">D</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">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#D7" title="MEMBERED:def.7">MEMBERED:def 7</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="c5">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#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c3">C</font> or <font color="Maroon" title="c5">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#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c4">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:153"/>
<font color="Maroon" title="c5">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#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c3">C</font>
 ; <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="c5">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#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c4">D</font></span><br/>

<a NAME="E3:153"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">c1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st <br/>( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Olive" title="b2">c1</font> &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Olive" title="b2">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">C</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:153"/>
<font color="Maroon" title="c5">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#K13" title="MEMBER_1:func.13">**</a> <font color="Maroon" title="c4">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:153"><span class="lab"><font color="Green" title="E72">A1</font></span></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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