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

<b>let </b><font color="Maroon">IIG</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</a> non <a href="msualg_1.html#V2">void</a> <a href="msafree2.html#V2">Circuit-like</a> <a href="msafree2.html#V5">monotonic</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">SCS</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">IIG</font>;<br/><b>let </b><font color="Maroon">InpFs</font> be   <a href="circuit1.html#NM2">InputFuncs</a> of <font color="Maroon">SCS</font>;<br/><b>let </b><font color="Maroon">iv</font> be    <a href="msafree2.html#M1">InputValues</a> of <font color="Maroon">SCS</font>;<br/>







<b>assume </b><a NAME="E1:27"/><i><font color="Green">E42</font></i>: 
(  <a href="funct_6.html#K10">commute</a> <font color="Maroon">InpFs</font> is <a href="funct_1.html#V3">constant</a> &amp; not  <a href="msafree2.html#K2">InputVertices</a> <font color="Maroon">IIG</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">iv</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_6.html#K10">commute</a> <font color="Maroon">InpFs</font></span>)</span> <a href="funct_1.html#K1">.</a> 0 )
 ;<br/>

<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <font color="Maroon">SCS</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">IIG</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E2:27"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K7">depth</a> <font color="Maroon">SCS</font>
 ;<br/>

<a NAME="E3:27"/>
 <a href="circuit1.html#K6">depth</a> <font color="Maroon">v</font>,<font color="Maroon">SCS</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="circuit1.html#K7">depth</a> <font color="Maroon">SCS</font>
 
<b>by </b><i><a class="ref" href="circuit1.html#T18">CIRCUIT1:18</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K9" target="_self">Computation</a> <font color="Maroon">s</font>,<font color="Maroon">InpFs</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K5" target="_self">IGValue</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font>
 <b>by </b><i>, , </i>;<br/>


</div>
