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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="E1:16"/><i><font color="Green">E12</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; <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="E2:16"/><i><font color="Green">E13</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> 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>8</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="E3:16"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</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> &amp; <font color="Maroon">c<sub>8</sub></font> is <a href="circcmb3.html#V1" target="_self">stabilizing</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>5</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:16"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <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>
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is <a href="circcmb3.html#V1" target="_self">stabilizing</a>
 ;<br/>

<a NAME="E6:16"/>
 <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="circcmb3.html#E4:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="circcmb3.html#E5:16"><i><font color="Green">E16</font></i></a>, <a class="ref" href="circcmb3.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E7:16"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E8:16"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="circcmb3.html#V1" target="_self">stabilizing</a>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="circcmb3.html#E4:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="circcmb3.html#E5:16"><i><font color="Green">E16</font></i></a>, <a class="ref" href="circcmb3.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circcmb3.html#K1" target="_self">Result</a> <font color="Maroon">c<sub>7</sub></font></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> = 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>7</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>
<b>by </b><i><a class="ref" href="circcmb3.html#T2" target="_self">Th2</a></i>
<br/>.= 
 <a href="facirc_1.html#K9">Following</a> <font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><a href="circcmb3.html#K2" target="_self">stabilization-time</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green">E13</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="circcmb2.html#T14">CIRCCMB2:14</a></i>
<br/>.= 
 <a href="circcmb3.html#K1" target="_self">Result</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="circcmb3.html#E7:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="circcmb3.html#T5" target="_self">Th5</a></i>
;<br/><br/>


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