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<b>consider </b><font color="Maroon" title="c5">a1</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><b> such that </b><br/><a NAME="E2:19_1_1"/><i><font color="Green" title="E7">A1</font></i>: 
for <font color="Olive" title="b1">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <font color="Maroon" title="c3">L1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Olive" title="b1">z</font>
 <b>by </b><i><a class="ref" href="cfdiff_1.html#D4" target="_self" title="CFDIFF_1:def.4">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">a2</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><b> such that </b><br/><a NAME="E4:19_1_1"/><i><font color="Green" title="E8">A2</font></i>: 
for <font color="Olive" title="b1">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds  <font color="Maroon" title="c4">L2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Olive" title="b1">z</font>
 <b>by </b><i><a class="ref" href="cfdiff_1.html#D4" target="_self" title="CFDIFF_1:def.4">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">z</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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="c3">L1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c7">z</font></span><br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">z</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T76" title="CFUNCT_1:th.76">CFUNCT_1:76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c7">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">z</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:19_1_1"><i><font color="Green" title="E7">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c7">z</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c7">z</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:19_1_1"><i><font color="Green" title="E8">A2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">a1</font> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <font color="Maroon" title="c6">a2</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c7">z</font>

; <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="E6:19_1_1"/>
<font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c4">L2</font> is   <a href="cfdiff_1.html#NM2" title="CFDIFF_1:NM.2">C_LINEAR</a>
 <b>by </b><i><a class="ref" href="cfdiff_1.html#D4" target="_self" title="CFDIFF_1:def.4">Def4</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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