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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font></span><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" title="c1">G</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> or  not <font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">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" title="c1">G</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font></span><br/><div class="add"><a NAME="E2:6_1_1"/><b>then </b>
 <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">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="msafree2.html#D1" target="_self" title="MSAFREE2:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E3:6_1_1"/>
 <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</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><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" title="E4">A1</font></i>: 
not <font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font></span><br/><div class="add"><a NAME="E2:6_1_2"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">G</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/><a NAME="E3:6_1_2"/><i><font color="Green" title="E6">A3</font></i>: 
 <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">v</font> where <font color="Olive" title="b1">v</font> is   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">G</font> : <font color="Olive" title="b1">v</font> is <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E1:6_1_2"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="msafree2.html#D1" target="_self" title="MSAFREE2:def.1">Def1</a></i>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font> )</span><br/><b>assume </b><a NAME="E4:6_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K1" title="MSAFREE2:func.1">SortsWithConstants</a> <font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font></span><br/><b>then consider </b><font color="Maroon" title="c3">x'</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E6:6_1_2"/><i><font color="Green" title="E7">A4</font></i>: 
( <font color="Maroon" title="c3">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c3">x'</font> is <a href="msualg_2.html#V1" title="MSUALG_2:attr.1">with_const_op</a> )
 <b>by </b><i><a class="txt" href="#E3:6_1_2"><i><font color="Green" title="E6">A3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c4">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E8:6_1_2"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E9:6_1_2"/><i><font color="Green" title="E8">A5</font></i>: 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x'</font>
 <b>by </b><i><a class="txt" href="#E6:6_1_2"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="msualg_2.html#D2" title="MSUALG_2:def.2">MSUALG_2:def 2</a></i>;<br/><b>thus </b><a NAME="E10:6_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="#E2:6_1_2"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="#E6:6_1_2"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="#E9:6_1_2"><i><font color="Green" title="E8">A5</font></i></a>, <a class="ref" href="funct_2.html#T6" title="FUNCT_2:th.6">FUNCT_2:6</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><b>end;</b></div></div><b>end;</b></div>

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