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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msafree2.html#V2" title="MSAFREE2:attr.2">Circuit-like</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E12">A1</font></i>: 
(  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <font color="Maroon" title="c2">S2</font> &amp; <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c2">S2</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">A1</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">S1</font>;<br/><b>let </b><font color="Maroon" title="c5">A2</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c6">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c3">S</font>;<br/>





<b>assume </b><a NAME="E2:16"/><i><font color="Green" title="E13">A2</font></i>: 
( <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">A2</font> &amp; <font color="Maroon" title="c6">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c5">A2</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c7">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">A</font>;<br/><b>let </b><font color="Maroon" title="c8">s1</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>;<br/>



<b>assume </b><a NAME="E3:16"/><i><font color="Green" title="E14">A3</font></i>: 
( <font color="Maroon" title="c8">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c8">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> )
 ;<br/>

<b>let </b><font color="Maroon" title="c9">s2</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:16"/><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green" title="E16">A5</font></i>: 
<font color="Maroon" title="c9">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a>
 ;<br/>

<a NAME="E6:16"/>
 <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c9">s2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:16"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:16"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="circcmb3.html#T11" target="_self" title="CIRCCMB3:th.11">Th11</a></i>;<br/>
<a NAME="E7:16"/><b>then </b><i><font color="Green" title="E17">A6</font></i>: 
 <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c7">s</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E8:16"/>
<font color="Maroon" title="c7">s</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:16"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:16"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="circcmb3.html#T10" target="_self" title="CIRCCMB3:th.10">Th10</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c7">s</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> = 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c7">s</font></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>
<b>by </b><i><a class="ref" href="circcmb3.html#T2" target="_self" title="CIRCCMB3:th.2">Th2</a></i>
<br/>.= 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c8">s1</font>,<span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c7">s</font></span>)</span>
<b>by </b><i><a class="txt" href="circcmb3.html#E1:16"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:16"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:16"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="circcmb2.html#T14" title="CIRCCMB2:th.14">CIRCCMB2:14</a></i>
<br/>.= 
 <a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Maroon" title="c8">s1</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:16"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E7:16"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="circcmb3.html#T5" target="_self" title="CIRCCMB3:th.5">Th5</a></i>
;<br/><br/>


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