<?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> 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">v</font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">IIG</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>let </b><font color="Maroon">p</font> be  <a href="trees_3.html#V6">DTree-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a>;<br/>









<b>assume </b><a NAME="E1:13"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">v</font> <a href="hidden.html#R2">in</a>  <a href="msafree2.html#K4">InnerVertices</a> <font color="Maroon">IIG</font> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> holds <br/><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K4" target="_self">IGTree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font></span>)</span>,<font color="Maroon">iv</font> ) )
 ;<br/>

<b>set </b><font color="Maroon">X</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font>;<br/>
<b>set </b><font color="Maroon">o</font> =  <a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font>;<br/>
<b>set </b><font color="Maroon">U1</font> =  <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font>;<br/>
<a NAME="E2:13"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:13_1"/><b>then </b>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K4" target="_self">IGTree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>,<font color="Maroon">iv</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:13_1"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">p''</font> = <font color="Maroon">p</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <b>by </b><i>, <a class="ref" href="msafree2.html#T7">MSAFREE2:7</a></i>;<br/>
<a NAME="E5:13"/><i><font color="Green">E44</font></i>: 
 <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K10">FreeOper</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msafree.html#D16">MSAFREE:def 16</a></i>;<br/>
<a NAME="E6:13"/><i><font color="Green">E45</font></i>: 
 <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <span class="p3">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">IIG</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_1.html#D9">MSUALG_1:def 9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p''</font> as    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> <b>by </b><i>, <a class="ref" href="msafree.html#T8">MSAFREE:8</a></i>;<br/>
<a NAME="E8:13"/><i><font color="Green">E47</font></i>: 
 <a href="msaterm.html#K2">Sym</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1">roots</a> <font color="Maroon">p'</font>
 
<b>by </b><i>, , <a class="ref" href="msafree.html#T10">MSAFREE:10</a></i>;<br/>
<a NAME="E9:13"/>
 <a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K10">FreeOper</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msafree.html#D16">MSAFREE:def 16</a></i>;<br/>
<b>then </b> <a href="msualg_1.html#K5">Den</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="msafree.html#K10">FreeOper</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
 <a href="msafree.html#K9">DenOp</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font>
<b>by </b><i><a class="ref" href="msafree.html#D15">MSAFREE:def 15</a></i>
;<br/>
<b>then </b><i><font color="Green">E48</font></i>: <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p2">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> = 
<span class="p1">(<span class="default"><a href="msaterm.html#K2">Sym</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">p'</font>
<b>by </b><i>, <a class="ref" href="msafree.html#D14">MSAFREE:def 14</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p'</font>
<b>by </b><i><a class="ref" href="msafree.html#D11">MSAFREE:def 11</a></i>
;<br/>
<i><font color="Green">E49</font></i>: the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">IIG</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span> = 
 <a href="msualg_1.html#K2">the_result_sort_of</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
<br/>.= 
<font color="Maroon">v</font>
<b>by </b><i>, <a class="ref" href="msafree2.html#D7">MSAFREE2:def 7</a></i>
;<br/>
<a NAME="E13:13"/><i><font color="Green">E51</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K4">Result</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<a NAME="E14:13"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">IIG</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">IIG</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
 <a href="msualg_1.html#K4">Result</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">IIG</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">IIG</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">t</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font> <b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:13_6"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/><b>set </b><font color="Maroon">v1</font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font>;<br/><a NAME="E2:13_6"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K4" target="_self">IGTree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>,<font color="Maroon">iv</font>
 <b>by </b><i>, </i>;<br/><b>then reconsider </b><font color="Maroon">ek</font> = <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K6">FreeEnv</a> <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span> ;<br/><b>take </b><font color="Maroon">ek</font> = <font color="Maroon">ek</font>;<br/><b>thus </b><a NAME="E4:13_6"/>
<font color="Maroon">ek</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 ;<br/><b>consider </b><font color="Maroon">e1</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">SCS</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span><b> such that </b><br/><a NAME="E6:13_6"/><i><font color="Green">E60</font></i>: 
(  <a href="card_1.html#K4">card</a> <font color="Maroon">e1</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K4">size</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>,<font color="Maroon">SCS</font> &amp; <font color="Maroon">ek</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" target="_self">Fix_inp_ext</a> <font color="Maroon">iv</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p4">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e1</font> )
 <b>by </b><i>, </i>;<br/><b>thus </b><a NAME="E7:13_6"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">ek</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K4">size</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>,<font color="Maroon">SCS</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E18:13"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="circuit1.html#K4">size</a> <font color="Maroon">v</font>,<font color="Maroon">SCS</font>
 
<b>by </b><i>, <a class="ref" href="circuit1.html#T17">CIRCUIT1:17</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:13_7"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:13_7"/><b>then </b>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="circuit2.html#K4" target="_self">IGTree</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p3">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span>,<font color="Maroon">iv</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:13_7"/>
<font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" target="_self">Fix_inp_ext</a> <font color="Maroon">iv</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p4">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E20:13"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="circuit2.html#K3" target="_self">Fix_inp_ext</a> <font color="Maroon">iv</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E21:13"/>
 <a href="circuit2.html#K4" target="_self">IGTree</a> <font color="Maroon">v</font>,<font color="Maroon">iv</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="msafree2.html#K5">action_at</a> <font color="Maroon">v</font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">IIG</font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">p</font>
 <b>by </b><i>, </i>;<br/>


</div>
