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

<b>let </b><font color="Maroon" title="c1">IAlph</font>, <font color="Maroon" title="c2">OAlph</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">tfsm</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font>;<br/>





<b>set </b><font color="Maroon" title="c4">M</font> = <font color="Maroon" title="c3">tfsm</font>;<br/>
<b>let </b><font color="Maroon" title="c5">cTran</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font>;<br/><b>let </b><font color="Maroon" title="c6">cOFun</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c2">OAlph</font>;<br/><b>let </b><font color="Maroon" title="c7">cInitS</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:98"/><i><font color="Green" title="E72">A1</font></i>: 
<font color="Maroon" title="c5">cTran</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>and </b><br/><a NAME="E2:98"/><i><font color="Green" title="E73">A2</font></i>: 
<font color="Maroon" title="c6">cOFun</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>and </b><br/><a NAME="E3:98"/><i><font color="Green" title="E74">A3</font></i>: 
<font color="Maroon" title="c7">cInitS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">cm</font> =  <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #);<br/>
<b>let </b><font color="Maroon" title="c9">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D9" target="_self" title="FSM_1:def.9">FSM_1:def 9</a><br/>

<b>set </b><font color="Maroon" title="c10">ma</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<b>set </b><font color="Maroon" title="c11">cma</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<div><i><font color="Green" title="E75">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:98_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 <b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/><b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> implies <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 );<br/><a NAME="E2:98_1"/><i><font color="Green" title="E76">A5</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 <b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:98_1"/><i><font color="Green" title="E77">A6</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:98_1_1"/><i><font color="Green" title="E78">A7</font></i>: 
( <font color="Maroon" title="c12">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> implies <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> )
 ;<br/>

<b>assume </b><a NAME="E2:98_1_1"/>
<font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/>

<a NAME="E3:98_1_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E4:98_1_1"/><b>then </b><i><font color="Green" title="E79">A8</font></i>: 
( <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font> &amp; <font color="Maroon" title="c12">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:98_1_1"/><i><font color="Green" title="E80">A9</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">j</font> or (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">j</font> &amp; <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:98_1_1_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">j</font> or 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font> )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E5:98_1_1"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_1"><b>suppose </b></a><a NAME="E1:98_1_1_1_1"/><i><font color="Green" title="E81">A10</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">j</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>
<b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:98"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="fsm_1.html#E1:98_1_1_1_1"><i><font color="Green" title="E81">A10</font></i></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_2"><b>suppose </b></a><a NAME="E1:98_1_1_1_2"/><i><font color="Green" title="E81">A11</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">j</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c13">mwj</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font>, <font color="Maroon" title="c14">mqj</font>, <font color="Maroon" title="c15">mqj1</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font><b> such that </b><br/><a NAME="E3:98_1_1_1_2"/><i><font color="Green" title="E82">A12</font></i>: 
( <font color="Maroon" title="c13">mwj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c14">mqj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Maroon" title="c15">mqj1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c13">mwj</font> <a href="fsm_1.html#K1" title="FSM_1:func.1">-succ_of</a> <font color="Maroon" title="c14">mqj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">mqj1</font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:98_1_1"><i><font color="Green" title="E79">A8</font></i></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/><a NAME="E4:98_1_1_1_2"/>
 ex <font color="Olive" title="b1">cmwj</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font> ex <font color="Olive" title="b2">cmqj</font>, <font color="Olive" title="b3">cmqj1</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #) st <br/>( <font color="Olive" title="b1">cmwj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Olive" title="b2">cmqj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">j</font> &amp; <font color="Olive" title="b3">cmqj1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b1">cmwj</font> <a href="fsm_1.html#K1" title="FSM_1:func.1">-succ_of</a> <font color="Olive" title="b2">cmqj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">cmqj1</font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:98_1_1"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="fsm_1.html#E1:98_1_1_1_2"><i><font color="Green" title="E81">A11</font></i></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E5:98_1_1_1_2"/>
<span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="fsm_1.html#E1:98_1_1"><i><font color="Green" title="E78">A7</font></i></a>, <a class="txt" href="fsm_1.html#E4:98_1_1"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="fsm_1.html#E1:98_1_1_1_2"><i><font color="Green" title="E81">A11</font></i></a>, <a class="txt" href="fsm_1.html#E3:98_1_1_1_2"><i><font color="Green" title="E82">A12</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>thus </b><a NAME="E4:98_1"/>
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">j</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="fsm_1.html#E2:98_1"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="fsm_1.html#E3:98_1"><i><font color="Green" title="E77">A6</font></i></a>);</i><br/></div><b>end;</b></div>
<a NAME="E5:98"/><b>then </b><i><font color="Green" title="E76">A13</font></i>: 
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> 
 
<b>by </b><i><a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>
<b>set </b><font color="Maroon" title="c12">mr</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<b>set </b><font color="Maroon" title="c13">cmr</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:98_2"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font> )
 <b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><b>let </b><font color="Maroon" title="c14">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E2:98_2"/><i><font color="Green" title="E77">A14</font></i>: 
<font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span>
 ;<br/><a NAME="E3:98_2"/><b>then </b><i><font color="Green" title="E78">A15</font></i>: 
<font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">w</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:98_2"/><i><font color="Green" title="E79">A16</font></i>: 
<font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:98_2"><i><font color="Green" title="E77">A14</font></i></a>, <a class="ref" href="finseq_2.html#T9" title="FINSEQ_2:th.9">FINSEQ_2:9</a></i>;<br/><a NAME="E5:98_2"/><b>then </b>
<font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:98"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E6:98_2"/><b>then </b><i><font color="Green" title="E80">A17</font></i>: 
( <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font> &amp; <font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">IAlph</font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:98_2"><i><font color="Green" title="E78">A15</font></i></a>, <a class="ref" href="finseq_2.html#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></i>;<br/><a NAME="E7:98_2"/>
<font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:98"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="fsm_1.html#E4:98_2"><i><font color="Green" title="E79">A16</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:98_2"/><b>then </b>
<span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></i>;<br/><a NAME="E9:98_2"/><b>then </b><i><font color="Green" title="E81">A18</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:98_2"><i><font color="Green" title="E80">A17</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><b>thus </b><span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font> = 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:98_2"><i><font color="Green" title="E78">A15</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c6">cOFun</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:98"><i><font color="Green" title="E76">A13</font></i></a>, <a class="txt" href="fsm_1.html#E9:98_2"><i><font color="Green" title="E81">A18</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">j</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:98_2"><i><font color="Green" title="E78">A15</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:98"/>
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <span class="p1">(<span class="default"><a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c5">cTran</font>,<font color="Maroon" title="c6">cOFun</font>,<font color="Maroon" title="c7">cInitS</font> #),<font color="Maroon" title="c9">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>


</div>
