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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">o2</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:28"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/>

<a NAME="E2:28"/><i><font color="Green">E33</font></i>: 
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:28"/><i><font color="Green">E38</font></i>: 
( the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:28"/>
 <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o2</font>
 <b>by </b><i>, , , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>

<b>thus </b><a NAME="E5:28"/>
 <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">o2</font>
 <b>by </b><i>, , , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>


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