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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:113"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E3:113"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E1:113"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="partfun1.html#T168" target="_self">Th168</a></i>;<br/>
<a NAME="E5:113"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="partfun1.html#V1" target="_self">total</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E3:113"><i><font color="Green">E56</font></i></a>, <a class="ref" href="partfun1.html#T169" target="_self">Th169</a>, <a class="ref" href="partfun1.html#T171" target="_self">Th171</a></i>;<br/>
<b>hence </b><a NAME="E6:113"/>
<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="partfun1.html#T158" target="_self">Th158</a></i>;<br/>


</div>
