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<b>let </b><font color="Maroon">f1</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">f2</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>reconsider </b><font color="Maroon">X'</font> = <font color="Maroon">X</font> as    <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">o'</font> = <font color="Maroon">o</font> as   <a href="circcomb.html#NM1">Gate</a> of <span class="p1">(<span class="default"><font color="Maroon">X'</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span> ;<br/>
<b>assume </b><a NAME="E3:24_1_1"/><i><font color="Green">E39</font></i>: 
( ( for <font color="Olive">X'</font> being   <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>  st <font color="Olive">X'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> holds <br/>for <font color="Olive">o'</font> being  <a href="circcomb.html#NM1">Gate</a> of <span class="p1">(<span class="default"><font color="Olive">X'</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span>  st <font color="Olive">o'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> holds <br/><font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">o'</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> ) &amp; ( for <font color="Olive">X'</font> being   <a href="msaterm.html#M3">SetWithCompoundTerm</a> of <font color="Maroon">S</font>,<font color="Maroon">V</font>  st <font color="Olive">X'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> holds <br/>for <font color="Olive">o'</font> being  <a href="circcomb.html#NM1">Gate</a> of <span class="p1">(<span class="default"><font color="Olive">X'</font> <a href="circtrm1.html#K1" target="_self">-CircuitStr</a> </span>)</span>  st <font color="Olive">o'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> holds <br/><font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">o'</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> ) &amp; not <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 ;<br/>

<a NAME="E4:24_1_1"/><b>then </b>
( <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">o'</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> &amp; <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">o'</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span> )
 
;<br/>
<b>hence </b><a NAME="E5:24_1_1"/>
contradiction
 <b>by </b><i/>;<br/>


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