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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>;<br/><b>let </b><font color="Maroon" title="c2">E</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">E</font>;<br/>





<b>assume </b><a NAME="E1:67"/>
<font color="Maroon" title="c3">A</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c1">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">ES</font> being  non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:67"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c3">A</font> is  <a href="msualg_6.html#V1" title="MSUALG_6:attr.1">feasible</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c4">ES</font>
 <b>by </b><i><a class="ref" href="algspec1.html#D7" target="_self" title="ALGSPEC1:def.7">Def7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">B</font> = <font color="Maroon" title="c3">A</font> as    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c4">ES</font> <b>by </b><i><a class="txt" href="algspec1.html#E3:67"><i><font color="Green" title="E50">A1</font></i></a></i>;<br/>
<a NAME="E5:67"/><i><font color="Green" title="E51">A2</font></i>: 
<font color="Maroon" title="c1">S</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c4">ES</font>
 
<b>by </b><i><a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">Def5</a></i>;<br/>
<a NAME="E6:67"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">ES</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">E</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:67"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">E</font>
 <b>by </b><i><a class="txt" href="algspec1.html#E5:67"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="instalg1.html#T11" title="INSTALG1:th.11">INSTALG1:11</a></i>;<br/>

<a NAME="E8:67"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c4">ES</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">E</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:67"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">E</font>
 <b>by </b><i><a class="txt" href="algspec1.html#E5:67"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="instalg1.html#T11" title="INSTALG1:th.11">INSTALG1:11</a></i>;<br/>


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