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<b>let </b><font color="Maroon">S</font> be  <a href="instalg1.html#V1" target="_self">feasible</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">T</font> be    <a href="instalg1.html#M1" target="_self">Subsignature</a> of <font color="Maroon">S</font>;<br/>



<a NAME="E1:18"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E2:18"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">T</font> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">T</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:18"/>
( the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> <a href="partfun1.html#K2">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">T</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="partfun1.html#K2">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">T</font> )
 <b>by </b><i><a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>;<br/>


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