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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <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="xboole_0.html#K1">{}</a> ;<br/>



<b>assume </b><a NAME="E1:109"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:109"/><i><font color="Green">E54</font></i>: 
 <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="xboole_0.html#K1">{}</a> <b> such that </b><br/><a NAME="E5:109"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:109"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1" target="_self">total</a>
 <b>and </b><br/><a NAME="E7:109"/>
<font color="Maroon">c<sub>2</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="txt" href="partfun1.html#E2:109"><i><font color="Green">E54</font></i></a>, <a class="ref" href="partfun1.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E8:109"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T62" target="_self">Th62</a></i>;<br/>
<b>hence </b><a NAME="E9:109"/>
contradiction
 <b>by </b><i><a class="txt" href="partfun1.html#E1:109"><i><font color="Green">E53</font></i></a>, <a class="txt" href="partfun1.html#E6:109"><i><font color="Green">E55</font></i></a>, <a class="ref" href="partfun1.html#D4" target="_self">Def4</a></i>;<br/>


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