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<span class="kw">let </span><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">S9</font> be   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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>  st <font color="Olive" title="b1">A</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c2">S9</font> holds <br/><font color="Maroon" title="c1">S</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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">S9</font> implies <font color="Maroon" title="c1">S</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S9</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:73"/>
<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">S9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S9</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">E</font> being   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S9</font><span class="kw"> such that </span><br/><a NAME="E3:73"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#D7" target="_self" title="ALGSPEC1:def.7">Def7</a></span>;<br/>
<a NAME="E4:73"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c2">S9</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">Def5</a></span>;<br/>
<a NAME="E5:73"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
 <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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>, the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>, the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">E</font>, the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c4">E</font>, the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c4">E</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:73"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="algspec1.html#T62" target="_self" title="ALGSPEC1:th.62">Th65</a></span>;<br/>
<a NAME="E6:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A4</font></span>: 
 the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S9</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">ResultSort</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="instalg1.html#T11" title="INSTALG1:th.11">INSTALG1:11</a></span>;<br/>
<a NAME="E7:73"/>
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S9</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E5:73"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="instalg1.html#T11" title="INSTALG1:th.11">INSTALG1:11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:73"/>
<font color="Maroon" title="c2">S9</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E5:73"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E6:73"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="instalg1.html#T10" title="INSTALG1:th.10">INSTALG1:10</a>, <a class="ref" href="instalg1.html#T13" title="INSTALG1:th.13">INSTALG1:13</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">ALGSPEC1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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