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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="E1:34"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> &amp;  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</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#K2" title="MSAFREE2:func.2">InputVertices</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">C1</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">C2</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">C</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="E2:34"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c4">C1</font> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a> <font color="Maroon" title="c5">C2</font> &amp; <font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c5">C2</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c7">s1</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c4">C1</font>;<br/><b>let </b><font color="Maroon" title="c8">s2</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c5">C2</font>;<br/><b>let </b><font color="Maroon" title="c9">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c6">C</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E3:34"/><i><font color="Green" title="E11">A3</font></i>: 
( <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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="c2">S2</font> )
 <b>and </b><br/><a NAME="E4:34"/><i><font color="Green" title="E12">A4</font></i>: 
( <font color="Maroon" title="c7">s1</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> &amp; <font color="Maroon" title="c8">s2</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a> )
 ;<br/>

<a NAME="E5:34"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="circcmb2.html#E1:34"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a>, <a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E6:34"/><b>then </b>
<font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">s2</font>
 
<b>by </b><i><a class="txt" href="circcmb2.html#E3:34"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="funct_4.html#T74" title="FUNCT_4:th.74">FUNCT_4:74</a></i>;<br/>
<b>then </b><font color="Maroon" title="c9">s</font> = 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c7">s1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">s2</font>
<b>by </b><i><a class="txt" href="circcmb2.html#E4:34"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c7">s1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c8">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="circcmb2.html#E4:34"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a></i>
<br/>.= 
 <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c9">s</font>
<b>by </b><i><a class="txt" href="circcmb2.html#E1:34"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="circcmb2.html#E2:34"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="circcmb2.html#E3:34"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="circcomb.html#T39" title="CIRCCOMB:th.39">CIRCCOMB:39</a></i>
;<br/>
<b>hence </b><a NAME="E8:34"/>
<font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c9">s</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a><br/>


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