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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ;<br/>



<b>assume </b><a NAME="E1:105"/><i><font color="Green" title="E51">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:105"/><i><font color="Green" title="E52">A2</font></i>: 
 <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K5" title="PARTFUN1:func.5">TotFuncs</a> <font color="Maroon" title="c2">f</font>;<br/>
<b>consider </b><font color="Maroon" title="c4">g'</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <b> such that </b><br/><a NAME="E5:105"/>
<font color="Maroon" title="c4">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font>
 <b>and </b><br/><a NAME="E6:105"/><i><font color="Green" title="E53">A3</font></i>: 
<font color="Maroon" title="c4">g'</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 <b>and </b><br/><a NAME="E7:105"/>
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c4">g'</font>
 <b>by </b><i><a class="txt" href="partfun1.html#E2:105"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="partfun1.html#D7" target="_self" title="PARTFUN1:def.7">Def7</a></i>;<br/>
<a NAME="E8:105"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T62" target="_self" title="PARTFUN1:th.62">Th62</a></i>;<br/>
<b>hence </b><a NAME="E9:105"/>
contradiction
 <b>by </b><i><a class="txt" href="partfun1.html#E1:105"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="partfun1.html#E6:105"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="partfun1.html#D4" target="_self" title="PARTFUN1:def.4">Def4</a></i>;<br/>


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