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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>thus </b><a NAME="E1:60"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a> implies  <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a>
 ;<br/>

<a NAME="E2:60_1"/>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T38" target="_self">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:60_1"/>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a>
 <b>by </b><i><a class="txt" href="rfunct_1.html#E1:60_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="rfunct_1.html#T67" target="_self">Th67</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:60"/><i><font color="Green">E39</font></i>: 
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a>
 ;<br/>

<a NAME="E3:60"/>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T38" target="_self">Th38</a></i>;<br/>
<b>hence </b><a NAME="E4:60"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a>
 <b>by </b><i><a class="txt" href="rfunct_1.html#E2:60"><i><font color="Green">E39</font></i></a>, <a class="ref" href="rfunct_1.html#T67" target="_self">Th67</a></i>;<br/>


</div>
