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<b>let </b><font color="Maroon">S1</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> , <font color="Maroon">S2</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> , <font color="Maroon">S</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="E1:42"/><i><font color="Green">E39</font></i>: 
(  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">S1</font> <a href="xboole_0.html#R1">misses</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">S2</font> &amp; <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S1</font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S2</font> )
 ;<br/>

<b>let </b><font color="Maroon">A1</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">A2</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E2:42"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">A1</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">A2</font> )
 ;<br/>

<b>let </b><font color="Maroon">n1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">s'</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A1</font>;<br/><b>let </b><font color="Maroon">s''</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A2</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E3:42"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">s'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> &amp;  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s'</font>,<font color="Maroon">n1</font> is <a href="circuit2.html#V1">stable</a> )
 <b>and </b><br/><a NAME="E4:42"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">s''</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<font color="Maroon">n1</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp;  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s''</font>,<font color="Maroon">n2</font> is <a href="circuit2.html#V1">stable</a> )
 ;<br/>

<a NAME="E5:42"/><i><font color="Green">E45</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
 
<b>by </b><i>, <a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">s1</font> = <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<font color="Maroon">n1</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>, <font color="Maroon">s0</font> = <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> as   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A1</font> <b>by </b><i>, <a class="ref" href="circcomb.html#T33">CIRCCOMB:33</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s2</font> = <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<font color="Maroon">n1</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> as   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">A2</font> <b>by </b><i>, , <a class="ref" href="circcomb.html#T33">CIRCCOMB:33</a></i>;<br/>
<a NAME="E8:42"/><i><font color="Green">E46</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 
<b>by </b><i>, <a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a>, <a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E9:42"/><i><font color="Green">E48</font></i>: 
(  <a href="facirc_1.html#K9">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<font color="Maroon">n1</font></span>)</span>,<font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span> &amp;  <a href="facirc_1.html#K9">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s0</font>,<font color="Maroon">n1</font></span>)</span>,<font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s0</font>,<span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T13">FACIRC_1:13</a></i>;<br/>
<a NAME="E10:42"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s0</font>,<font color="Maroon">n1</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E11:42"/><b>then </b><i><font color="Green">E76</font></i>: 
( <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</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">S1</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s1</font>,<font color="Maroon">n2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</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">S2</font> <a href="hidden.html#R1">=</a>  <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s2</font>,<font color="Maroon">n2</font> )
 
<b>by </b><i>, , , , , </i>;<br/>
<b>then </b> <a href="circuit2.html#K6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p2">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span></span>)</span> = 
<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">s2</font>,<font color="Maroon">n2</font></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">s1</font>,<font color="Maroon">n2</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="circcomb.html#T40">CIRCCOMB:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s2</font>,<font color="Maroon">n2</font></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">s1</font>,<font color="Maroon">n2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s2</font>,<font color="Maroon">n2</font></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">s1</font>,<span class="p2">(<span class="default"><font color="Maroon">n2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="facirc_1.html#T12">FACIRC_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s2</font>,<font color="Maroon">n2</font></span>)</span> <a href="funct_4.html#K1">+*</a> <font color="Maroon">s1</font>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="facirc_1.html#K9">Following</a> <font color="Maroon">s2</font>,<font color="Maroon">n2</font></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">s1</font>,<font color="Maroon">n2</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
 <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_4.html#T74">FUNCT_4:74</a></i>
;<br/>
<b>hence </b><a NAME="E13:42"/>
 <a href="facirc_1.html#K9">Following</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n2</font></span>)</span> is <a href="circuit2.html#V1">stable</a>
 <b>by </b><i><a class="ref" href="circuit2.html#D6">CIRCUIT2:def 6</a></i>;<br/>


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