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

<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">SC</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font>  st <font color="Olive" title="b1">SC</font> <a href="partfun2.html#K4" title="PARTFUN2:func.4">--&gt;</a> <font color="Olive" title="b2">d</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> holds <br/><font color="Olive" title="b1">SC</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> </span><br/><b>let </b><font color="Maroon" title="c3">SC</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font>  st <font color="Maroon" title="c3">SC</font> <a href="partfun2.html#K4" title="PARTFUN2:func.4">--&gt;</a> <font color="Olive" title="b1">d</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> holds <br/><font color="Maroon" title="c3">SC</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> </span><br/><b>let </b><font color="Maroon" title="c4">d</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">SC</font> <a href="partfun2.html#K4" title="PARTFUN2:func.4">--&gt;</a> <font color="Maroon" title="c4">d</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> implies <font color="Maroon" title="c3">SC</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>  )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c3">SC</font> <a href="partfun2.html#K4" title="PARTFUN2:func.4">--&gt;</a> <font color="Maroon" title="c4">d</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c3">SC</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:39"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">SC</font> <a href="partfun2.html#K4" title="PARTFUN2:func.4">--&gt;</a> <font color="Maroon" title="c4">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="txt" href="partfun2.html#E1:39"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
contradiction
 <b>by </b><i><a class="txt" href="partfun2.html#E2:39"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="funcop_1.html#T16" title="FUNCOP_1:th.16">FUNCOP_1:16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
