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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="circcomb.html#V1">unsplit</a> <a href="circcomb.html#V2">gate`1=arity</a> <a href="circcomb.html#V3">gate`2isBoolean</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circcomb.html#V4">gate`2=den</a> <a href="circcomb.html#V6">Boolean</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>









<b>assume </b><a NAME="E1:67"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">g</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> as   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">S</font> ;<br/>
<i><font color="Green">E35</font></i>:  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">g</font> = 
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D6">MSUALG_1:def 6</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i>, <a class="ref" href="circcomb.html#D8">CIRCCOMB:def 8</a></i>
;<br/>
<a NAME="E4:67"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">g</font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">g</font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
 <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">g</font> = 
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
<br/>.= 
<font color="Maroon">g</font>
<b>by </b><i>, <a class="ref" href="circcomb.html#T52">CIRCCOMB:52</a></i>
;<br/>
<b>hence </b><a NAME="E6:67"/>
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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