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<b>let </b><font color="Maroon">S0</font> be  non <a href="struct_0.html#V3">empty</a> <a href="msualg_1.html#V1">strict</a> non <a href="msualg_1.html#V2">void</a> <a href="msualg_2.html#V2">all-with_const_op</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2">OSSign</a> <font color="Maroon">S0</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_2.html#D3">MSUALG_2:def 3</a><br/>



<b>reconsider </b><font color="Maroon">s1</font> = <font color="Maroon">s</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S0</font> <b>by </b><i><a class="ref" href="osalg_1.html#D6">OSALG_1:def 6</a></i>;<br/>
<a NAME="E2:8"/>
<font color="Maroon">s1</font> is <a href="msualg_2.html#V1">with_const_op</a>
 
<b>by </b><i><a class="ref" href="msualg_2.html#D3">MSUALG_2:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">o</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S0</font><b> such that </b><br/><a NAME="E4:8"/><i><font color="Green">E25</font></i>: 
( the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> )
 <b>by </b><i><a class="ref" href="msualg_2.html#D2">MSUALG_2:def 2</a></i>;<br/>
<a NAME="E5:8"/>
( <font color="Maroon">o</font> is    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2">OSSign</a> <font color="Maroon">S0</font></span>)</span> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2">OSSign</a> <font color="Maroon">S0</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2">OSSign</a> <font color="Maroon">S0</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> )
 
<b>by </b><i>, <a class="ref" href="osalg_1.html#D6">OSALG_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E6:8"/>
<font color="Maroon">s</font> is <a href="msualg_2.html#V1">with_const_op</a>
 <b>by </b><i><a class="ref" href="msualg_2.html#D2">MSUALG_2:def 2</a></i>;<br/>


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