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<b>let </b><font color="Maroon" title="c6">S1</font>, <font color="Maroon" title="c7">S2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c8">u</font> = <font color="Maroon" title="c4">v</font> as   <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="circtrm1.html#T4" target="_self" title="CIRCTRM1:th.4">Th4</a></i>;<br/>
<b>assume </b><a NAME="E2:22_1_1"/><i><font color="Green" title="E14">A1</font></i>: 
( ( for <font color="Olive" title="b1">u</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> holds <br/><font color="Maroon" title="c6">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Olive" title="b1">u</font></span>)</span> ) &amp; ( for <font color="Olive" title="b1">u</font> being  <a href="msaterm.html#NM1" title="MSATERM:NM.1">Term</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> holds <br/><font color="Maroon" title="c7">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Olive" title="b1">u</font></span>)</span> ) &amp; not <font color="Maroon" title="c6">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">S2</font> )
 ;<br/>

<a NAME="E3:22_1_1"/><b>then </b>
( <font color="Maroon" title="c6">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Maroon" title="c8">u</font></span>)</span> &amp; <font color="Maroon" title="c7">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="msaterm.html#K7" title="MSATERM:func.7">the_sort_of</a> <font color="Maroon" title="c8">u</font></span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E4:22_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="circtrm1.html#E2:22_1_1"><i><font color="Green" title="E14">A1</font></i></a></i>;<br/>


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