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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="facirc_1.html#K20" target="_self">MajorityICirc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K20" target="_self">MajorityICirc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E1:110"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span><a href="tarski.html#K4">]</a></span> as    <a href="struct_0.html#M1">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T47" target="_self">Th47</a></i>;<br/>
<a NAME="E3:110"/><i><font color="Green">E67</font></i>: 
 <a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p2">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="circcomb.html#T10">CIRCCOMB:10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>16</sub></font> as    <a href="struct_0.html#M1">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E5:110"/><i><font color="Green">E68</font></i>: 
 <a href="facirc_1.html#K20" target="_self">MajorityICirc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <a href="circcomb.html#K4">+*</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T25" target="_self">Th25</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>13</sub></font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> as   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K10" target="_self">1GateCircuit</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E7:110"/><i><font color="Green">E69</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T43" target="_self">Th43</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>20</sub></font> as   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K18" target="_self">MajorityIStr</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="txt" href="facirc_1.html#E3:110"><i><font color="Green">E67</font></i></a>, <a class="ref" href="facirc_1.html#T20" target="_self">Th20</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>,<a href="facirc_1.html#K3" target="_self">'&amp;'</a> </span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="facirc_1.html#E3:110"><i><font color="Green">E67</font></i></a>, <a class="txt" href="facirc_1.html#E5:110"><i><font color="Green">E68</font></i></a>, <a class="ref" href="circcomb.html#T72">CIRCCOMB:72</a></i>
<br/>.= 
<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#T50" target="_self">Th50</a></i>
<br/>.= 
<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="facirc_1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="facirc_1.html#E7:110"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<a href="facirc_1.html#K3" target="_self">'&amp;'</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="facirc_1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="facirc_1.html#K15" target="_self">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span></span><a href="facirc_1.html#K6" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="facirc_1.html#E7:110"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="facirc_1.html#E1:110"><i><font color="Green">E66</font></i></a>, <a class="ref" href="facirc_1.html#D6" target="_self">Def6</a></i>
;<br/>


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