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<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:6_1"/>
( <font color="Maroon">G</font> is <a href="msualg_1.html#V2">void</a> or  not <font color="Maroon">G</font> is <a href="msualg_1.html#V2">void</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_1"><b>suppose </b></a><a NAME="E1:6_1_1"/>
<font color="Maroon">G</font> is <a href="msualg_1.html#V2">void</a>
 ;<br/><div class="add"><a NAME="E2:6_1_1"/><b>then </b>
 <a href="msafree2.html#K1" target="_self">SortsWithConstants</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:6_1_1"/>
 <a href="msafree2.html#K1" target="_self">SortsWithConstants</a> <font color="Maroon">G</font> <a href="tarski.html#R1">c=</a>  <a href="msafree2.html#K3" target="_self">InnerVertices</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="6_1_2"><b>suppose </b></a><a NAME="E1:6_1_2"/><i><font color="Green">E29</font></i>: 
not <font color="Maroon">G</font> is <a href="msualg_1.html#V2">void</a>
 ;<br/><div class="add"><a NAME="E2:6_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/><a NAME="E3:6_1_2"/><i><font color="Green">E33</font></i>: 
 <a href="msafree2.html#K1" target="_self">SortsWithConstants</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">v</font> where <font color="Olive">v</font> is   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">G</font> : <font color="Olive">v</font> is <a href="msualg_2.html#V1">with_const_op</a> </span>}</span> 
 <b>by </b><i>, </i>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E4:6_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K1" target="_self">SortsWithConstants</a> <font color="Maroon">G</font>
 ;<br/><b>then consider </b><font color="Maroon">x'</font> being   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E6:6_1_2"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">x'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x'</font> is <a href="msualg_2.html#V1">with_const_op</a> )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">o</font> being   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E8:6_1_2"/>
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E9:6_1_2"/><i><font color="Green">E39</font></i>: 
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font>
 <b>by </b><i>, <a class="ref" href="msualg_2.html#D2">MSUALG_2:def 2</a></i>;<br/><a NAME="E10:6_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">G</font>
 <b>by </b><i>, , , <a class="ref" href="funct_2.html#T6">FUNCT_2:6</a></i>;<br/><b>hence </b><a NAME="E11:6_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K3" target="_self">InnerVertices</a> <font color="Maroon">G</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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