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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  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green">E19</font></i>: 
(  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>





<b>assume </b><a NAME="E2:45"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>





<b>assume </b><a NAME="E3:45"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:45"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E5:45"/><i><font color="Green">E23</font></i>: 
(  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font> is <a href="circuit2.html#V1">stable</a> &amp;  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>8</sub></font> is <a href="circuit2.html#V1">stable</a> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/>
<a NAME="E6:45"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb2.html#E1:45"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcmb2.html#E3:45"><i><font color="Green">E21</font></i></a>, <a class="ref" href="circcmb2.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E7:45"/>
<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#R1">tolerates</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<a NAME="E8:45"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="ref" href="circcomb.html#T9">CIRCCOMB:9</a>, <a class="ref" href="circcomb.html#T23">CIRCCOMB:23</a>, <a class="ref" href="circcomb.html#T26">CIRCCOMB:26</a></i>;<br/>
<a NAME="E9:45"/><b>then </b><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb2.html#E1:45"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcmb2.html#E4:45"><i><font color="Green">E22</font></i></a>, <a class="ref" href="circcmb2.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E10:45"/>
(  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>7</sub></font> is <a href="circuit2.html#V1">stable</a> &amp;  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>8</sub></font> is <a href="circuit2.html#V1">stable</a> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="circcmb2.html#E5:45"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xxreal_0.html#T25">XXREAL_0:25</a></i>;<br/>
<a NAME="E11:45"/><b>then </b><i><font color="Green">E26</font></i>: 
(  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> is <a href="circuit2.html#V1">stable</a> &amp;  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> is <a href="circuit2.html#V1">stable</a> )
 
<b>by </b><i><a class="ref" href="circcmb2.html#T4" target="_self">Th4</a></i>;<br/>
<b>thus </b> <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E1:45"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcmb2.html#E3:45"><i><font color="Green">E21</font></i></a>, <a class="txt" href="circcmb2.html#E4:45"><i><font color="Green">E22</font></i></a>, <a class="ref" href="circcmb2.html#T22" target="_self">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E11:45"><i><font color="Green">E26</font></i></a>, <a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>10</sub></font>,<span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E11:45"><i><font color="Green">E26</font></i></a>, <a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a></i>
<br/>.= 
 <a href="circuit2.html#K6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>9</sub></font>,<span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E1:45"><i><font color="Green">E19</font></i></a>, <a class="txt" href="circcmb2.html#E2:45"><i><font color="Green">E20</font></i></a>, <a class="txt" href="circcmb2.html#E6:45"><i><font color="Green">E24</font></i></a>, <a class="txt" href="circcmb2.html#E9:45"><i><font color="Green">E25</font></i></a>, <a class="ref" href="circcomb.html#T39">CIRCCOMB:39</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a><br/>


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