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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/>





<b>thus </b><a NAME="E1:110"/>
( <font color="Maroon">f</font> is <a href="partfun1.html#V1" target="_self">total</a> implies  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:110_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> is <a href="partfun1.html#V1" target="_self">total</a>
 ;<br/>

<a NAME="E2:110_1"/>
for <font color="Olive">g</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> iff <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:110_1_1"/>
( <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> implies <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:110_1_1_1"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:110_1_1_1"/><b>then </b>
 ex <font color="Olive">g'</font> being  <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font> st <br/>( <font color="Olive">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> &amp; <font color="Olive">g'</font> is <a href="partfun1.html#V1" target="_self">total</a> &amp; <font color="Maroon">f</font> <a href="partfun1.html#R1" target="_self">tolerates</a> <font color="Olive">g'</font> )
 
<b>by </b><i><a class="txt" href="partfun1.html#E13"><i><font color="Green">Lemma49</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:110_1_1_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T32" target="_self">Th32</a>, <a class="txt" href="partfun1.html#E4"><i><font color="Green">Lemma46</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:110_1_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> implies <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="partfun1.html#T32" target="_self">Th32</a>, <a class="txt" href="partfun1.html#E13"><i><font color="Green">Lemma49</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:110_1"/>
 <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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

<b>assume </b><a NAME="E2:110"/>
 <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E3:110"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K5" target="_self">TotFuncs</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:110"/>
<font color="Maroon">f</font> is <a href="partfun1.html#V1" target="_self">total</a>
 <b>by </b><i><a class="ref" href="partfun1.html#T27" target="_self">Th27</a></i>;<br/>


</div>
