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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> implies for <font color="Olive" title="b1">S</font> being 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>   st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b2">A1</font> being <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/> for <font color="Olive" title="b3">A2</font> being <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>  st <font color="Olive" title="b2">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b3">A2</font> holds <br/>for <font color="Olive" title="b4">A</font> being <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="Olive" title="b1">S</font>  st <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b3">A2</font> holds <br/>for <font color="Olive" title="b5">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b4">A</font><br/> for <font color="Olive" title="b6">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A1</font>  st <font color="Olive" title="b6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">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="Olive" title="b6">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b7">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A2</font>  st <font color="Olive" title="b7">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="Olive" title="b5">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b6">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> &amp; <font color="Olive" title="b7">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b5">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="Olive" title="b6">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="Olive" title="b7">s2</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:15"/><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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being 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>   st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> holds <br/>for <font color="Olive" title="b2">A1</font> being <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/> for <font color="Olive" title="b3">A2</font> being <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>  st <font color="Olive" title="b2">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b3">A2</font> holds <br/>for <font color="Olive" title="b4">A</font> being <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="Olive" title="b1">S</font>  st <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b3">A2</font> holds <br/>for <font color="Olive" title="b5">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b4">A</font><br/> for <font color="Olive" title="b6">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A1</font>  st <font color="Olive" title="b6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">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="Olive" title="b6">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b7">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A2</font>  st <font color="Olive" title="b7">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="Olive" title="b5">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b6">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> &amp; <font color="Olive" title="b7">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b5">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="Olive" title="b6">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="Olive" title="b7">s2</font></span>)</span></span><br/>

<b>let </b><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> implies for <font color="Olive" title="b1">A1</font> being <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/> for <font color="Olive" title="b2">A2</font> being <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>  st <font color="Olive" title="b1">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b3">A</font> being <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>  st <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b4">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A</font><br/> for <font color="Olive" title="b5">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A1</font>  st <font color="Olive" title="b5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">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="Olive" title="b5">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b6">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A2</font>  st <font color="Olive" title="b6">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="Olive" title="b4">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b5">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> &amp; <font color="Olive" title="b6">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b4">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="Olive" title="b5">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="Olive" title="b6">s2</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green" title="E13">A2</font></i>: 
<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#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being <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/> for <font color="Olive" title="b2">A2</font> being <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>  st <font color="Olive" title="b1">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b3">A</font> being <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>  st <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b2">A2</font> holds <br/>for <font color="Olive" title="b4">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b3">A</font><br/> for <font color="Olive" title="b5">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A1</font>  st <font color="Olive" title="b5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">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="Olive" title="b5">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b6">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A2</font>  st <font color="Olive" title="b6">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="Olive" title="b4">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b5">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> &amp; <font color="Olive" title="b6">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b4">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="Olive" title="b5">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="Olive" title="b6">s2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A2</font> being <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>  st <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Olive" title="b1">A2</font> holds <br/>for <font color="Olive" title="b2">A</font> being <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>  st <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Olive" title="b1">A2</font> holds <br/>for <font color="Olive" title="b3">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b4">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">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="Olive" title="b4">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b5">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A2</font>  st <font color="Olive" title="b5">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="Olive" title="b3">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b4">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> &amp; <font color="Olive" title="b5">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b3">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="Olive" title="b4">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="Olive" title="b5">s2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies for <font color="Olive" title="b1">A</font> being <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>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">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="Olive" title="b3">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b4">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b4">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="Olive" title="b2">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b3">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> &amp; <font color="Olive" title="b4">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b2">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="Olive" title="b3">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="Olive" title="b4">s2</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E3:15"/><i><font color="Green" title="E14">A3</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <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>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> <a href="circcomb.html#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b3">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">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="Olive" title="b3">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b4">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b4">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="Olive" title="b2">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b3">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> &amp; <font color="Olive" title="b4">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b2">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="Olive" title="b3">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="Olive" title="b4">s2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font> implies for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">A</font><br/> for <font color="Olive" title="b2">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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="Olive" title="b2">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b3">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b3">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="Olive" title="b1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b3">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b1">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="Olive" title="b2">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="Olive" title="b3">s2</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E4:15"/><i><font color="Green" title="E15">A4</font></i>: 
<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#K5" title="CIRCCOMB:func.5">+*</a> <font color="Maroon" title="c5">A2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">A</font><br/> for <font color="Olive" title="b2">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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="Olive" title="b2">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b3">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b3">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="Olive" title="b1">s</font>,<span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b3">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Olive" title="b1">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="Olive" title="b2">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="Olive" title="b3">s2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">A1</font>  st <font color="Olive" title="b1">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="Olive" title="b1">s1</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/>for <font color="Olive" title="b2">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b2">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="Olive" title="b1">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> &amp; <font color="Olive" title="b2">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <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="Olive" title="b1">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="Olive" title="b2">s2</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies for <font color="Olive" title="b1">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b1">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> &amp; <font color="Olive" title="b1">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <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="Olive" title="b1">s2</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E5:15"/><i><font color="Green" title="E16">A5</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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s2</font> being  <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>  st <font color="Olive" title="b1">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> &amp; <font color="Olive" title="b1">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> holds <br/> <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="Olive" title="b1">s2</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c9">st1</font> =  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font>;<br/>
<b>let </b><font color="Maroon" title="c10">s2</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">A2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">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> &amp; <font color="Maroon" title="c10">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> implies  <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="c10">s2</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E6:15"/><i><font color="Green" title="E17">A6</font></i>: 
( <font color="Maroon" title="c10">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> &amp; <font color="Maroon" title="c10">s2</font> is <a href="circcmb3.html#V1" title="CIRCCMB3:attr.1">stabilizing</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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="c10">s2</font></span>)</span></span><br/>

<a NAME="E7:15"/><i><font color="Green" title="E18">A7</font></i>: 
<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#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="circcmb3.html#E6:15"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="circcmb3.html#T10" target="_self" title="CIRCCMB3:th.10">Th10</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">st2</font> =  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c10">s2</font>;<br/>
<a NAME="E8:15"/><i><font color="Green" title="E19">A8</font></i>: 
(  <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="c8">s1</font></span>)</span> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> &amp;  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s2</font>,<span class="p1">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c10">s2</font></span>)</span> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> )
 
<b>by </b><i><a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="circcmb3.html#E6:15"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="circcmb3.html#D5" target="_self" title="CIRCCMB3:def.5">Def5</a></i>;<br/>
<a NAME="E9:15"/><b>then </b><i><font color="Green" title="E20">A9</font></i>: 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<span class="p1">(<span class="default"><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> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c10">s2</font></span>)</span></span>)</span> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 
<b>by </b><i><a class="txt" href="circcmb3.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="circcmb3.html#E6:15"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="circcmb2.html#T20" title="CIRCCMB2:th.20">CIRCCMB2:20</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c12">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="c10">s2</font></span>)</span> implies  not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Olive">b<sub>1</sub></font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> )</span><br/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E21">A10</font></i>: 
<font color="Maroon" title="c12">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="c10">s2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Olive">b<sub>1</sub></font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_1"/>
(  <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> <font color="Maroon" title="c12">n</font> or <font color="Maroon" title="c12">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_1"><b>suppose </b></a><a NAME="E1:15_1_1_1"/>
 <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> <font color="Maroon" title="c12">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Olive">b<sub>1</sub></font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c13">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:15_1_1_1"/><i><font color="Green" title="E22">A11</font></i>: 
<font color="Maroon" title="c12">n</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> <font color="Maroon" title="c13">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">m</font> = <font color="Maroon" title="c13">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E5:15_1_1_1"/>
<font color="Maroon" title="c14">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c10">s2</font>
 <b>by </b><i><a class="txt" href="circcmb3.html#E1:15_1"><i><font color="Green" title="E21">A10</font></i></a>, <a class="txt" href="circcmb3.html#E3:15_1_1_1"><i><font color="Green" title="E22">A11</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E6:15_1_1_1"/><b>then </b><i><font color="Green" title="E23">A12</font></i>: 
not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">m</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 <b>by </b><i><a class="txt" href="circcmb3.html#E6:15"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="circcmb3.html#D5" target="_self" title="CIRCCMB3:def.5">Def5</a></i>;<br/><a NAME="E7:15_1_1_1"/>
 <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="c8">s1</font></span>)</span> <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="c1">S1</font>
 <b>by </b><i><a class="txt" href="circcmb3.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="circcmb2.html#T14" title="CIRCCMB2:th.14">CIRCCMB2:14</a></i>;<br/><b>then </b> <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c10">s2</font>,<font color="Maroon" title="c14">m</font> = 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <span class="p2">(<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="p3">(<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>,<font color="Maroon" title="c14">m</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="c2">S2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E6:15"><i><font color="Green" title="E17">A6</font></i></a>, <a class="txt" href="circcmb3.html#E8:15"><i><font color="Green" title="E19">A8</font></i></a>, <a class="ref" href="circcmb2.html#T19" title="CIRCCMB2:th.19">CIRCCMB2:19</a></i>
<br/>.= 
<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>,<font color="Maroon" title="c12">n</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="c2">S2</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:15_1_1_1"><i><font color="Green" title="E22">A11</font></i></a>, <a class="ref" href="facirc_1.html#T13" title="FACIRC_1:th.13">FACIRC_1:13</a></i>
;<br/><b>hence </b><a NAME="E9:15_1_1_1"/>
not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c12">n</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 <b>by </b><i><a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E6:15_1_1_1"><i><font color="Green" title="E23">A12</font></i></a>, <a class="ref" href="circcmb2.html#T18" title="CIRCCMB2:th.18">CIRCCMB2:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1_2"><b>suppose </b></a><a NAME="E1:15_1_1_2"/>
<font color="Maroon" title="c12">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="circcmb3.html#K2" title="CIRCCMB3:func.2">stabilization-time</a> <font color="Maroon" title="c8">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Olive">b<sub>1</sub></font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a></span><br/><div class="add"><a NAME="E2:15_1_1_2"/><b>then </b><i><font color="Green" title="E22">A13</font></i>: 
not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c8">s1</font>,<font color="Maroon" title="c12">n</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 <b>by </b><i><a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="circcmb3.html#D5" target="_self" title="CIRCCMB3:def.5">Def5</a></i>;<br/><a NAME="E3:15_1_1_2"/>
<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>,<font color="Maroon" title="c12">n</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c8">s1</font>,<font color="Maroon" title="c12">n</font>
 <b>by </b><i><a class="txt" href="circcmb3.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E5:15"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="circcmb2.html#T14" title="CIRCCMB2:th.14">CIRCCMB2:14</a></i>;<br/><b>hence </b><a NAME="E4:15_1_1_2"/>
not  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c12">n</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 <b>by </b><i><a class="txt" href="circcmb3.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="circcmb3.html#E3:15"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="circcmb3.html#E4:15"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="circcmb3.html#E2:15_1_1_2"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="circcmb2.html#T18" title="CIRCCMB2:th.18">CIRCCMB2:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15"/>
 <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="c10">s2</font></span>)</span>
 <b>by </b><i><a class="txt" href="circcmb3.html#E7:15"><i><font color="Green" title="E18">A7</font></i></a>, <a class="txt" href="circcmb3.html#E9:15"><i><font color="Green" title="E20">A9</font></i></a>, <a class="ref" href="circcmb3.html#D5" target="_self" title="CIRCCMB3:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
