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<b>let </b><font color="Maroon">S1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">S2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">v</font> as   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:22_1_1"/><i><font color="Green">E36</font></i>: 
( ( for <font color="Olive">u</font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>  st <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> holds <br/><font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">u</font></span>)</span> ) &amp; ( for <font color="Olive">u</font> being  <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>  st <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> holds <br/><font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Olive">u</font></span>)</span> ) &amp; not <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font> )
 ;<br/>

<a NAME="E3:22_1_1"/><b>then </b>
( <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">u</font></span>)</span> &amp; <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7">the_sort_of</a> <font color="Maroon">u</font></span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E4:22_1_1"/>
contradiction
 <b>by </b><i/>;<br/>


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