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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font>,<font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="circcomb.html#M1" target="_self">FinSeqLen</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>;<br/>









<b>set </b><font color="Maroon">S</font> =  <a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">A</font> =  <a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">IV</font> =  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>;<br/>
<a NAME="E1:100"/>
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><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></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#T3" target="_self">Th3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">v</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="subset_1.html#M2">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:100"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><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></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">o</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 <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:100"/><i><font color="Green">E24</font></i>: 
<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> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span> <a href="circuit1.html#K3">depends_on_in</a> <font color="Maroon">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit2.html#D5">CIRCUIT2:def 5</a></i>;<br/>
<a NAME="E6:100"/>
 <a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:100"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="msafree2.html#D7">MSAFREE2:def 7</a></i>;<br/>
<a NAME="E8:100"/>
 <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E9:100"/><b>then </b>
<font color="Maroon">o</font> <a href="circuit1.html#K3">depends_on_in</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="circuit1.html#D3">CIRCUIT1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:100"/>
<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><a class="ref" href="circcomb.html#D2" target="_self">Def2</a>, , </i>;<br/>


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