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<b>let </b><font color="Maroon" title="c1">b</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  iff <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K8" title="FINSEQOP:func.8">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span>,<a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a>  )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">c1</font>, <font color="Maroon" title="c3">c2</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K8" title="FINSEQOP:func.8">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span>,<a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a> </span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font></span><br/><b>thus </b><a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font> = 
<font color="Maroon" title="c2">c1</font> <a href="binop_2.html#K4" title="BINOP_2:func.4">-</a> <font color="Maroon" title="c3">c2</font>
<b>by </b><i><a class="ref" href="binop_2.html#D4" title="BINOP_2:def.4">BINOP_2:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c2">c1</font> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c3">c2</font></span>)</span>

<br/>.= 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c3">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D3" title="BINOP_2:def.3">BINOP_2:def 3</a></i>
<br/>.= 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<span class="p1">(<span class="default"><a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D1" title="BINOP_2:def.1">BINOP_2:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K8" title="FINSEQOP:func.8">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span>,<a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a> </span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">c1</font>,<font color="Maroon" title="c3">c2</font>
<b>by </b><i><a class="ref" href="finseqop.html#T87" title="FINSEQOP:th.87">FINSEQOP:87</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="E2:2_1_1"/>
( <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_2.html#K28" title="BINOP_2:func.28">diffcomplex</a>  iff <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K8" title="FINSEQOP:func.8">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span>,<a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a>  )
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</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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