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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c2">X</font>;<br/><b>let </b><font color="Maroon" title="c4">p</font> be    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c5">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K8" title="CIRCCOMB:func.8">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span>;<br/>









<b>set </b><font color="Maroon" title="c6">S</font> =  <a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font>;<br/>
<b>set </b><font color="Maroon" title="c7">A</font> =  <a href="circcomb.html#K8" title="CIRCCOMB:func.8">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font>;<br/>
<b>set </b><font color="Maroon" title="c8">IV</font> =  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span>;<br/>
<a NAME="E1:98"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#T49" target="_self" title="CIRCCOMB:th.49">Th49</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">v</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:98"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D6" target="_self" title="CIRCCOMB:def.6">Def6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">o</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:98"/><i><font color="Green" title="E57">A1</font></i>: 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c9">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="circcomb.html#K8" title="CIRCCOMB:func.8">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c5">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit2.html#D5" title="CIRCUIT2:def.5">CIRCUIT2:def 5</a></i>;<br/>
<a NAME="E6:98"/>
 <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">v</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D6" target="_self" title="CIRCCOMB:def.6">Def6</a></i>;<br/>
<a NAME="E7:98"/><b>then </b><i><font color="Green" title="E58">A2</font></i>: 
 <a href="msafree2.html#K5" title="MSAFREE2:func.5">action_at</a> <font color="Maroon" title="c9">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o</font>
 
<b>by </b><i><a class="ref" href="msafree2.html#D7" title="MSAFREE2:def.7">MSAFREE2:def 7</a></i>;<br/>
<a NAME="E8:98"/>
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D6" target="_self" title="CIRCCOMB:def.6">Def6</a></i>;<br/>
<a NAME="E9:98"/><b>then </b>
<font color="Maroon" title="c10">o</font> <a href="circuit1.html#K3" title="CIRCUIT1:func.3">depends_on_in</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="ref" href="circuit1.html#D3" title="CIRCUIT1:def.3">CIRCUIT1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:98"/>
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="circcomb.html#E5:98"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="circcomb.html#E7:98"><i><font color="Green" title="E58">A2</font></i></a>, <a class="ref" href="circcomb.html#D14" target="_self" title="CIRCCOMB:def.14">Def14</a></i>;<br/>


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