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

<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:5"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">G</font>;<br/>

<b>assume </b><a NAME="E2:5"/><i><font color="Green" title="E4">A2</font></i>: 
 <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c3">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 ;<br/>

<a NAME="E3:5"/>
<font color="Maroon" title="c3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">G</font>
 
;<br/>
<a NAME="E4:5"/><b>then </b>
<font color="Maroon" title="c3">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:5"/><b>then </b><i><font color="Green" title="E5">A3</font></i>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="msafree2.html#E2:5"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>thus </b><a NAME="E6:5"/>
contradiction
 <b>by </b><i><a class="txt" href="msafree2.html#E1:5"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="msafree2.html#E5:5"><i><font color="Green" title="E5">A3</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>


</div>
