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<b>let </b><font color="Maroon">S</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">V</font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="msaterm.html#M1" target="_self">ArgumentSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">o</font>,<font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>









<b>assume </b><a NAME="E1:45"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:45"/><b>then </b>
 ex <font color="Olive">t</font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> &amp;  <a href="msaterm.html#K7" target="_self">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp;  <a href="msaterm.html#K7" target="_self">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:45"/>
for <font color="Olive">t</font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>  st <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> holds <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> &amp;  <a href="msaterm.html#K7" target="_self">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp;  <a href="msaterm.html#K7" target="_self">the_sort_of</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> )
 ;<br/>


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