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<b>let </b><font color="Maroon" title="c1">B</font>, <font color="Maroon" title="c2">C</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"> for <font color="Olive" title="b1">a</font> being <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds  <font color="Olive" title="b1">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></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> ; <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="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></span>)</span></span><br/>





<a NAME="E1:325"/><i><font color="Green" title="E141">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="member_1.html#T101" target="_self" title="MEMBER_1:th.101">Th101</a></i>;<br/>
<a NAME="E2:325"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="325_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">z</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#D7" title="MEMBERED:def.7">MEMBERED:def 7</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="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></span>)</span> or <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:325_1"/>
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></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="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span></span><br/>

<b>then consider </b><font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">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="E3:325_1"/><i><font color="Green" title="E142">A2</font></i>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <font color="Maroon" title="c6">c1</font>
 <b>and </b><br/><a NAME="E4:325_1"/><i><font color="Green" title="E143">A3</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font>
 <b>and </b><br/><a NAME="E5:325_1"/><i><font color="Green" title="E144">A4</font></i>: 
<font color="Maroon" title="c6">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c7">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="E7:325_1"/><i><font color="Green" title="E145">A5</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c7">c2</font>
 <b>and </b><br/><a NAME="E8:325_1"/><i><font color="Green" title="E146">A6</font></i>: 
<font color="Maroon" title="c7">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">B</font>
 <b>by </b><i><a class="txt" href="#E4:325_1"><i><font color="Green" title="E143">A3</font></i></a>, <a class="ref" href="member_1.html#T201" target="_self" title="MEMBER_1:th.201">Th201</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">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="E10:325_1"/><i><font color="Green" title="E147">A7</font></i>: 
<font color="Maroon" title="c6">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c8">c3</font>
 <b>and </b><br/><a NAME="E11:325_1"/><i><font color="Green" title="E148">A8</font></i>: 
<font color="Maroon" title="c8">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="txt" href="#E5:325_1"><i><font color="Green" title="E144">A4</font></i></a>, <a class="ref" href="member_1.html#T201" target="_self" title="MEMBER_1:th.201">Th201</a></i>;<br/>
<a NAME="E12:325_1"/><i><font color="Green" title="E149">A9</font></i>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">c2</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <font color="Maroon" title="c8">c3</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:325_1"><i><font color="Green" title="E142">A2</font></i></a>, <a class="txt" href="#E7:325_1"><i><font color="Green" title="E145">A5</font></i></a>, <a class="txt" href="#E10:325_1"><i><font color="Green" title="E147">A7</font></i></a></i>;<br/>
<a NAME="E13:325_1"/>
<font color="Maroon" title="c7">c2</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <font color="Maroon" title="c8">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font>
 
<b>by </b><i><a class="txt" href="#E8:325_1"><i><font color="Green" title="E146">A6</font></i></a>, <a class="txt" href="#E11:325_1"><i><font color="Green" title="E148">A8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E14:325_1"/>
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E12:325_1"><i><font color="Green" title="E149">A9</font></i></a>, <a class="ref" href="member_1.html#T199" target="_self" title="MEMBER_1:th.199">Th199</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>hence </b><a NAME="E3:325"/>
<font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="member_1.html#K6" title="MEMBER_1:func.6">++</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="member_1.html#K20" title="MEMBER_1:func.20">**</a> <font color="Maroon" title="c2">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:325"><i><font color="Green" title="E141">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
