<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="fdiff_1.html#NM2">LINEAR</a>;<br/>



<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:12"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="fdiff_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:12"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="fdiff_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E5:12"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a> )
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E6:12"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T66">RFUNCT_1:66</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E5:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="rfunct_1.html#T72">RFUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E2:12"><i><font color="Green">E8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E4:12"><i><font color="Green">E9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>4</sub></font> is   <a href="fdiff_1.html#NM2">LINEAR</a>
 <b>by </b><i><a class="txt" href="fdiff_1.html#E6:12"><i><font color="Green">E11</font></i></a>, <a class="ref" href="fdiff_1.html#D4" target="_self">Def4</a></i>;<br/>

<a NAME="E9:12"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="txt" href="fdiff_1.html#E5:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="rfunct_1.html#T66">RFUNCT_1:66</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E5:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="rfunct_1.html#T72">RFUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E2:12"><i><font color="Green">E8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_1.html#E4:12"><i><font color="Green">E9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>7</sub></font>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:12"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>4</sub></font> is   <a href="fdiff_1.html#NM2">LINEAR</a>
 <b>by </b><i><a class="txt" href="fdiff_1.html#E9:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="fdiff_1.html#D4" target="_self">Def4</a></i>;<br/>


</div>
