<?xml version="1.0"?>
<div class="add">

<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="E1:33"/><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">C1</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">C2</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">C</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="E2:33"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">C1</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">C2</font> )
 ;<br/>

<b>let </b><font color="Maroon">s1</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C1</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C</font>;<br/>



<b>assume </b><a NAME="E3:33"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">s1</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>
 ;<br/>

<a NAME="E4:33"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E5:33"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">C2</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">s2</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">S2</font> as   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">C2</font> <b>by </b><i>, <a class="ref" href="circcomb.html#T33">CIRCCOMB:33</a></i>;<br/>
<a NAME="E7:33"/>
 <a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s2</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s1</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="circcomb.html#T40">CIRCCOMB:40</a></i>;<br/>
<b>hence </b><a NAME="E8:33"/>
 <a href="circuit2.html#K6">Following</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</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>
 <b>by </b><i>, <a class="ref" href="funct_4.html#T24">FUNCT_4:24</a></i>;<br/>


</div>
