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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:148"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 <b>and </b><br/><a NAME="E2:148"/><i><font color="Green" title="E14">A2</font></i>: 
for <font color="Olive" title="b1">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font> holds <br/><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span>)</span>
 ;<br/>

<b>thus </b><a NAME="E3:148"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 <b>by </b><i><a class="txt" href="valued_1.html#E1:148"><i><font color="Green" title="E13">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D17" title="FUNCT_1:def.17">FUNCT_1:def 17</a><br/>

<b>let </b><font color="Maroon" title="c4">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E4:148"/><i><font color="Green" title="E15">A3</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<b>hence </b><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="valued_1.html#E2:148"><i><font color="Green" title="E14">A2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#T8" target="_self" title="VALUED_1:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="valued_1.html#K45" title="VALUED_1:func.45">-</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="valued_1.html#E1:148"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="valued_1.html#E4:148"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="valued_1.html#D1" target="_self" title="VALUED_1:def.1">Def1</a></i>
;<br/><br/>


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