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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> </span>)</span></span><br/><b>let </b><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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D13" title="MEMBERED:def.13">MEMBERED:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</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="member_1.html#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a>  ) )</span><br/>





<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</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="member_1.html#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a>  )</span>
<div class="add"><b>assume </b><a NAME="E1:167_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#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> </span>)</span></span><br/><b>then consider </b><font color="Maroon" title="c4">c</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> <b> such that </b><br/><a NAME="E3:167_1"/><i><font color="Green" title="E85">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <b>and </b><br/><a NAME="E4:167_1"/><i><font color="Green" title="E86">A2</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font>
 ;<br/><b>consider </b><font color="Maroon" title="c5">c1</font>, <font color="Maroon" title="c6">c2</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> <b> such that </b><br/><a NAME="E6:167_1"/><i><font color="Green" title="E87">A3</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c1</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c6">c2</font>
 <b>and </b><br/><a NAME="E7:167_1"/><i><font color="Green" title="E88">A4</font></i>: 
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E8:167_1"/><i><font color="Green" title="E89">A5</font></i>: 
<font color="Maroon" title="c6">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="txt" href="#E4:167_1"><i><font color="Green" title="E86">A2</font></i></a></i>;<br/><a NAME="E9:167_1"/><i><font color="Green" title="E90">A6</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c1</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">c2</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E3:167_1"><i><font color="Green" title="E85">A1</font></i></a>, <a class="txt" href="#E6:167_1"><i><font color="Green" title="E87">A3</font></i></a>, <a class="ref" href="xcmplx_1.html#T205" title="XCMPLX_1:th.205">XCMPLX_1:205</a></i>;<br/><a NAME="E10:167_1"/>
( <font color="Maroon" title="c5">c1</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="member_1.html#K4" title="MEMBER_1:func.4">""</a>  &amp; <font color="Maroon" title="c6">c2</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> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a>  )
 <b>by </b><i><a class="txt" href="#E7:167_1"><i><font color="Green" title="E88">A4</font></i></a>, <a class="txt" href="#E8:167_1"><i><font color="Green" title="E89">A5</font></i></a></i>;<br/><b>hence </b><a NAME="E11:167_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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E9:167_1"><i><font color="Green" title="E90">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:167"/>
<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#K4" title="MEMBER_1:func.4">""</a> </span>)</span> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">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> <b> such that </b><br/><a NAME="E4:167"/><i><font color="Green" title="E85">A7</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c5">c1</font>
 <b>and </b><br/><a NAME="E5:167"/><i><font color="Green" title="E86">A8</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> 
 <b>and </b><br/><a NAME="E6:167"/><i><font color="Green" title="E87">A9</font></i>: 
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> 
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">c2</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> <b> such that </b><br/><a NAME="E8:167"/><i><font color="Green" title="E88">A10</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c2</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <b>and </b><br/><a NAME="E9:167"/><i><font color="Green" title="E89">A11</font></i>: 
<font color="Maroon" title="c6">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E5:167"><i><font color="Green" title="E86">A8</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">c3</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> <b> such that </b><br/><a NAME="E11:167"/><i><font color="Green" title="E90">A12</font></i>: 
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c3</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 <b>and </b><br/><a NAME="E12:167"/><i><font color="Green" title="E91">A13</font></i>: 
<font color="Maroon" title="c7">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="txt" href="#E6:167"><i><font color="Green" title="E87">A9</font></i></a></i>;<br/>
<a NAME="E13:167"/><i><font color="Green" title="E92">A14</font></i>: 
<font color="Maroon" title="c6">c2</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c7">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> <a href="member_1.html#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="#E9:167"><i><font color="Green" title="E89">A11</font></i></a>, <a class="txt" href="#E12:167"><i><font color="Green" title="E91">A13</font></i></a></i>;<br/>
<a NAME="E14:167"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">c2</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c7">c3</font></span>)</span> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="#E4:167"><i><font color="Green" title="E85">A7</font></i></a>, <a class="txt" href="#E8:167"><i><font color="Green" title="E88">A10</font></i></a>, <a class="txt" href="#E11:167"><i><font color="Green" title="E90">A12</font></i></a>, <a class="ref" href="xcmplx_1.html#T205" title="XCMPLX_1:th.205">XCMPLX_1:205</a></i>;<br/>
<b>hence </b><a NAME="E15:167"/>
<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#K10" title="MEMBER_1:func.10">**</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="member_1.html#K4" title="MEMBER_1:func.4">""</a> 
 <b>by </b><i><a class="txt" href="#E13:167"><i><font color="Green" title="E92">A14</font></i></a></i>; <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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