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

<b>let </b><font color="Maroon" title="c1">OAlph</font>, <font color="Maroon" title="c2">IAlph</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="c2">IAlph</font>,<font color="Maroon" title="c1">OAlph</font>;<br/>





<b>set </b><font color="Maroon" title="c4">cTran</font> = 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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<a NAME="E1:97"/><i><font color="Green" title="E72">A1</font></i>: 
(  <a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="c2">IAlph</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">IAlph</font> )
 
<b>by </b><i><a class="ref" href="fsm_1.html#T67" target="_self" title="FSM_1:th.67">Th67</a></i>;<br/>
<a NAME="E2:97"/><b>then </b>
<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>,<font color="Maroon" title="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E3:97"/><b>then </b>
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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> is   <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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T38" title="FUNCT_2:th.38">FUNCT_2:38</a></i>;<br/>
<a NAME="E4:97"/><b>then </b><i><font color="Green" title="E73">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:97"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="fsm_1.html#K12" title="FSM_1:func.12">accessibleStates</a> <font color="Maroon" title="c3">tfsm</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:97_1"/><i><font color="Green" title="E74">A3</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
 ;<br/>

<a NAME="E2:97_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">q1</font> = <font color="Maroon" title="c5">x</font> as   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:97_1"><i><font color="Green" title="E74">A3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">d</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:97_1"/><i><font color="Green" title="E75">A4</font></i>: 
( <font color="Maroon" title="c7">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">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="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p3">(<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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d</font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:97_1"><i><font color="Green" title="E74">A3</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E6:97_1"/><i><font color="Green" title="E76">A5</font></i>: 
( <font color="Maroon" title="c7">d</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <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> &amp; <font color="Maroon" title="c7">d</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IAlph</font> )
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:97"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:97_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">q</font> = <font color="Maroon" title="c7">d</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  as   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:97"><i><font color="Green" title="E72">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">s</font> = <font color="Maroon" title="c7">d</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> <b>by </b><i><a class="txt" href="fsm_1.html#E4:97"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:97_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">I</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c3">tfsm</font>;<br/>
<a NAME="E9:97_1"/>
<font color="Maroon" title="c8">q</font> is <a href="fsm_1.html#V6" title="FSM_1:attr.6">accessible</a>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E6:97_1"><i><font color="Green" title="E76">A5</font></i></a>, <a class="ref" href="fsm_1.html#T67" target="_self" title="FSM_1:th.67">Th67</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c2">IAlph</font><b> such that </b><br/><a NAME="E11:97_1"/><i><font color="Green" title="E77">A6</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="c11">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c8">q</font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D21" target="_self" title="FSM_1:def.21">Def21</a></i>;<br/>
<a NAME="E12:97_1"/><i><font color="Green" title="E78">A7</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></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="c11">w</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/>
<b>set </b><font color="Maroon" title="c12">qsa</font> = <font color="Maroon" title="c8">q</font>,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<a NAME="E13:97_1"/><i><font color="Green" title="E79">A8</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <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> <font color="Maroon" title="c8">q</font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/>
<a NAME="E14:97_1"/><i><font color="Green" title="E80">A9</font></i>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">s</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E15:97_1"/>
1 <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> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E16:97_1"/><b>then </b><i><font color="Green" title="E81">A10</font></i>: 
 ex <font color="Olive" title="b1">wi</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">IAlph</font> ex <font color="Olive" title="b2">qi</font>, <font color="Olive" title="b3">qi1</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font> st <br/>( <font color="Olive" title="b1">wi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">qi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <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 &amp; <font color="Olive" title="b3">qi1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <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">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b1">wi</font> <a href="fsm_1.html#K1" title="FSM_1:func.1">-succ_of</a> <font color="Olive" title="b2">qi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">qi1</font> )
 
<b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/>
<a NAME="E17:97_1"/>
the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c3">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:97"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:97_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E18:97_1"/><b>then </b><i><font color="Green" title="E82">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <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">1 <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> <font color="Maroon" title="c6">q1</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E13:97_1"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="fsm_1.html#E14:97_1"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="fsm_1.html#E16:97_1"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="fsm_1.html#E4:97"><i><font color="Green" title="E73">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:97_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/>
<i><font color="Green" title="E83">A12</font></i>: <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 = 
<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="c11">w</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<b>by </b><i><a class="txt" href="fsm_1.html#E12:97_1"><i><font color="Green" title="E78">A7</font></i></a>, <a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

;<br/>
<a NAME="E20:97_1"/>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
;<br/>
<a NAME="E21:97_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 &amp; 2 <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> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E22:97_1"/><b>then </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>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <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> <font color="Maroon" title="c6">q1</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E11:97_1"><i><font color="Green" title="E77">A6</font></i></a>, <a class="txt" href="fsm_1.html#E18:97_1"><i><font color="Green" title="E82">A11</font></i></a>, <a class="txt" href="fsm_1.html#E19:97_1"><i><font color="Green" title="E83">A12</font></i></a>, <a class="ref" href="fsm_1.html#T22" target="_self" title="FSM_1:th.22">Th22</a></i>;<br/>
<a NAME="E23:97_1"/><b>then </b>
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="c11">w</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c9">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c6">q1</font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D3" target="_self" title="FSM_1:def.3">Def3</a></i>;<br/>
<a NAME="E24:97_1"/><b>then </b>
<font color="Maroon" title="c6">q1</font> is <a href="fsm_1.html#V6" title="FSM_1:attr.6">accessible</a>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D21" target="_self" title="FSM_1:def.21">Def21</a></i>;<br/>
<b>hence </b><a NAME="E25:97_1"/>
<font color="Maroon" title="c5">x</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>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:97"/>
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="c2">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> is   <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="c2">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>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:97"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>


</div>
