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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="msafree1.html#V1">disjoint_valued</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:75"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="algspec1.html#M4" target="_self">Algebra</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  non <a href="msualg_1.html#V2">void</a>  <a href="algspec1.html#M2" target="_self">Extension</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:75"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is  <a href="msualg_6.html#V1">feasible</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="algspec1.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E4:75"/>
( <font color="Maroon">c<sub>2</sub></font> is    <a href="instalg1.html#M1">Subsignature</a> of <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="msualg_1.html#G1">ManySortedSign</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G1">ManySortedSign</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>4</sub></font> #) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E3:75"><i><font color="Green">E56</font></i></a>, <a class="ref" href="algspec1.html#D5" target="_self">Def5</a>, <a class="ref" href="algspec1.html#T65" target="_self">Th65</a></i>;<br/>
<a NAME="E5:75"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#T11">INSTALG1:11</a>, <a class="ref" href="instalg1.html#T12">INSTALG1:12</a></i>;<br/>
<b>hence </b><a NAME="E6:75"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="instalg1.html#M1">Subsignature</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="instalg1.html#T14">INSTALG1:14</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="algspec1.html#D5" target="_self">ALGSPEC1:def 5</a><br/>


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