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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">S'</font> be  non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</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#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="msafree1.html#V1" title="MSAFREE1:attr.1">disjoint_valued</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/>





<b>assume </b><a NAME="E1:74"/>
<font color="Maroon" title="c3">A</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c2">S'</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">E</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="c2">S'</font><b> such that </b><br/><a NAME="E3:74"/><i><font color="Green" title="E55">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">E</font>
 <b>by </b><i><a class="ref" href="algspec1.html#D7" target="_self" title="ALGSPEC1:def.7">Def7</a></i>;<br/>
<a NAME="E4:74"/>
( <font color="Maroon" title="c2">S'</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c4">E</font> &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>,the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font>,the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font>,the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c4">E</font>,the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c4">E</font>,the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c4">E</font> #) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E3:74"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">Def5</a>, <a class="ref" href="algspec1.html#T65" target="_self" title="ALGSPEC1:th.65">Th65</a></i>;<br/>
<a NAME="E5:74"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">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="c1">S</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">S'</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">S'</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#T11" title="INSTALG1:th.11">INSTALG1:11</a>, <a class="ref" href="instalg1.html#T12" title="INSTALG1:th.12">INSTALG1:12</a></i>;<br/>
<b>hence </b><a NAME="E6:74"/>
<font color="Maroon" title="c2">S'</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="ref" href="instalg1.html#T14" title="INSTALG1:th.14">INSTALG1:14</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">ALGSPEC1:def 5</a><br/>


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