<?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">Ctfsm1</font>, <font color="Maroon" title="c4">Ctfsm2</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#V7" title="FSM_1:attr.7">connected</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>assume </b><a NAME="E1:115"/><i><font color="Green" title="E86">A1</font></i>: 
<font color="Maroon" title="c3">Ctfsm1</font>,<font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a> 
 ;<br/>

<b>set </b><font color="Maroon" title="c5">rtfsm1</font> =  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">rtfsm2</font> =  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font>;<br/>
<b>consider </b><font color="Maroon" title="c7">fsm1</font>, <font color="Maroon" title="c8">fsm2</font> being  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><b> such that </b><br/><a NAME="E3:115"/><i><font color="Green" title="E87">A2</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">fsm1</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">fsm2</font> &amp; <font color="Maroon" title="c7">fsm1</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a>  &amp; <font color="Maroon" title="c8">fsm2</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a>  )
 <b>by </b><i><a class="ref" href="fsm_1.html#T81" target="_self" title="FSM_1:th.81">Th81</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">ISfsm1</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c7">fsm1</font>;<br/>
<b>set </b><font color="Maroon" title="c10">ISfsm2</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c8">fsm2</font>;<br/>
<b>set </b><font color="Maroon" title="c11">ISrtfsm1</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">ISrtfsm2</font> = the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">Sfsm1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">fsm1</font>;<br/>
<b>set </b><font color="Maroon" title="c14">Sfsm2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">fsm2</font>;<br/>
<b>set </b><font color="Maroon" title="c15">Srtfsm1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c16">Srtfsm2</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span>;<br/>
<a NAME="E4:115"/><i><font color="Green" title="E88">A3</font></i>: 
 <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 
<b>by </b><i><a class="ref" href="fsm_1.html#T66" target="_self" title="FSM_1:th.66">Th66</a></i>;<br/>
<a NAME="E5:115"/><i><font color="Green" title="E89">A4</font></i>: 
<font color="Maroon" title="c7">fsm1</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:115_1"/>
not <font color="Maroon" title="c7">fsm1</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c17">q1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">fsm1</font><b> such that </b><br/><a NAME="E3:115_1"/><i><font color="Green" title="E90">A5</font></i>: 
not <font color="Maroon" title="c17">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#D22" target="_self" title="FSM_1:def.22">Def22</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">fsm1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span><b> such that </b><br/><a NAME="E5:115_1"/><i><font color="Green" title="E91">A6</font></i>: 
( <font color="Maroon" title="c18">Tf</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c7">fsm1</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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span> &amp; ( for <font color="Olive" title="b1">q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c7">fsm1</font><br/> for <font color="Olive" title="b2">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font> holds <br/> ( <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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="c7">fsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> &amp; the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c7">fsm1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> ) ) )
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#D19" target="_self" title="FSM_1:def.19">Def19</a></i>;<br/>
<a NAME="E6:115_1"/><i><font color="Green" title="E92">A7</font></i>: 
<font color="Maroon" title="c18">Tf</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E5:115_1"><i><font color="Green" title="E91">A6</font></i></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">q</font> = <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font>;<br/>
<a NAME="E7:115_1"/>
<font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</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#E4:115"><i><font color="Green" title="E88">A3</font></i></a>, <a class="ref" href="fsm_1.html#D22" target="_self" title="FSM_1:def.22">Def22</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c20">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><b> such that </b><br/><a NAME="E9:115_1"/><i><font color="Green" title="E93">A8</font></i>: 
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</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="E10:115_1"/><i><font color="Green" title="E94">A9</font></i>: 
( 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="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c20">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#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E11:115_1"/><b>then </b><i><font color="Green" title="E95">A10</font></i>: 
<font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c7">fsm1</font>,<font color="Maroon" title="c20">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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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 <span class="p2">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font></span>)</span>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">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#E5:115_1"><i><font color="Green" title="E91">A6</font></i></a>, <a class="ref" href="fsm_1.html#T60" target="_self" title="FSM_1:th.60">Th60</a></i>;<br/>
<a NAME="E12:115_1"/><i><font color="Green" title="E96">A11</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">Tf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">fsm1</font>
 
<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="E13:115_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="c7">fsm1</font>,<font color="Maroon" title="c20">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="c20">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/>
<a NAME="E14:115_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c7">fsm1</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E10:115_1"><i><font color="Green" title="E94">A9</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E15:115_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c7">fsm1</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>
 
<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="E16:115_1"/><b>then </b><i><font color="Green" title="E97">A12</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="c7">fsm1</font>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">Tf</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E12:115_1"><i><font color="Green" title="E96">A11</font></i></a>, <a class="ref" href="finseq_2.html#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E17:115_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <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="c7">fsm1</font>,<font color="Maroon" title="c20">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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E9:115_1"><i><font color="Green" title="E93">A8</font></i></a>, <a class="txt" href="fsm_1.html#E11:115_1"><i><font color="Green" title="E95">A10</font></i></a>, <a class="ref" href="fsm_1.html#D3" target="_self" title="FSM_1:def.3">Def3</a></i>;<br/>
<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="c7">fsm1</font>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font></span>)</span>
<b>by </b><i><a class="txt" href="fsm_1.html#E6:115_1"><i><font color="Green" title="E92">A7</font></i></a>, <a class="txt" href="fsm_1.html#E16:115_1"><i><font color="Green" title="E97">A12</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
<br/>.= 
<font color="Maroon" title="c17">q1</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E6:115_1"><i><font color="Green" title="E92">A7</font></i></a>, <a class="txt" href="fsm_1.html#E12:115_1"><i><font color="Green" title="E96">A11</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
;<br/>
<a NAME="E19:115_1"/><b>then </b>
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c7">fsm1</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c17">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/>
<b>hence </b><a NAME="E20:115_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:115_1"><i><font color="Green" title="E90">A5</font></i></a>, <a class="ref" href="fsm_1.html#D21" target="_self" title="FSM_1:def.21">Def21</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:115"/><i><font color="Green" title="E90">A13</font></i>: 
 <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 
<b>by </b><i><a class="ref" href="fsm_1.html#T66" target="_self" title="FSM_1:th.66">Th66</a></i>;<br/>
<a NAME="E7:115"/><i><font color="Green" title="E91">A14</font></i>: 
<font color="Maroon" title="c8">fsm2</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="115_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:115_2"/>
not <font color="Maroon" title="c8">fsm2</font> is <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c17">q1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">fsm2</font><b> such that </b><br/><a NAME="E3:115_2"/><i><font color="Green" title="E92">A15</font></i>: 
not <font color="Maroon" title="c17">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#D22" target="_self" title="FSM_1:def.22">Def22</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">fsm2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span><b> such that </b><br/><a NAME="E5:115_2"/><i><font color="Green" title="E93">A16</font></i>: 
( <font color="Maroon" title="c18">Tf</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c8">fsm2</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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span> &amp; ( for <font color="Olive" title="b1">q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c8">fsm2</font><br/> for <font color="Olive" title="b2">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font> holds <br/> ( <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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="c8">fsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> &amp; the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c8">fsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> ) ) )
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#D19" target="_self" title="FSM_1:def.19">Def19</a></i>;<br/>
<a NAME="E6:115_2"/><i><font color="Green" title="E94">A17</font></i>: 
<font color="Maroon" title="c18">Tf</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E5:115_2"><i><font color="Green" title="E93">A16</font></i></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">q</font> = <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font>;<br/>
<a NAME="E7:115_2"/>
<font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</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#E6:115"><i><font color="Green" title="E90">A13</font></i></a>, <a class="ref" href="fsm_1.html#D22" target="_self" title="FSM_1:def.22">Def22</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c20">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><b> such that </b><br/><a NAME="E9:115_2"/><i><font color="Green" title="E95">A18</font></i>: 
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</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="E10:115_2"/><i><font color="Green" title="E96">A19</font></i>: 
( 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="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c20">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#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E11:115_2"/><b>then </b><i><font color="Green" title="E97">A20</font></i>: 
<font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c8">fsm2</font>,<font color="Maroon" title="c20">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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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 <span class="p2">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font></span>)</span>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">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#E5:115_2"><i><font color="Green" title="E93">A16</font></i></a>, <a class="ref" href="fsm_1.html#T60" target="_self" title="FSM_1:th.60">Th60</a></i>;<br/>
<a NAME="E12:115_2"/><i><font color="Green" title="E98">A21</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">Tf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">fsm2</font>
 
<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="E13:115_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="c8">fsm2</font>,<font color="Maroon" title="c20">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="c20">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/>
<a NAME="E14:115_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c8">fsm2</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E10:115_2"><i><font color="Green" title="E96">A19</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E15:115_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c8">fsm2</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>
 
<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="E16:115_2"/><b>then </b><i><font color="Green" title="E99">A22</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="c8">fsm2</font>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">Tf</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E12:115_2"><i><font color="Green" title="E98">A21</font></i></a>, <a class="ref" href="finseq_2.html#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E17:115_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <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="c8">fsm2</font>,<font color="Maroon" title="c20">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="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E9:115_2"><i><font color="Green" title="E95">A18</font></i></a>, <a class="txt" href="fsm_1.html#E11:115_2"><i><font color="Green" title="E97">A20</font></i></a>, <a class="ref" href="fsm_1.html#D3" target="_self" title="FSM_1:def.3">Def3</a></i>;<br/>
<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="c8">fsm2</font>,<font color="Maroon" title="c20">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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">Tf</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</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="c18">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c17">q1</font></span>)</span>
<b>by </b><i><a class="txt" href="fsm_1.html#E6:115_2"><i><font color="Green" title="E94">A17</font></i></a>, <a class="txt" href="fsm_1.html#E16:115_2"><i><font color="Green" title="E99">A22</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
<br/>.= 
<font color="Maroon" title="c17">q1</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E6:115_2"><i><font color="Green" title="E94">A17</font></i></a>, <a class="txt" href="fsm_1.html#E12:115_2"><i><font color="Green" title="E98">A21</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>
;<br/>
<a NAME="E19:115_2"/><b>then </b>
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c8">fsm2</font>,<font color="Maroon" title="c20">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c17">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/>
<b>hence </b><a NAME="E20:115_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:115_2"><i><font color="Green" title="E92">A15</font></i></a>, <a class="ref" href="fsm_1.html#D21" target="_self" title="FSM_1:def.21">Def21</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:115"/><i><font color="Green" title="E92">A23</font></i>: 
(  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font>,<font color="Maroon" title="c3">Ctfsm1</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  &amp;  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font>,<font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  )
 
<b>by </b><i><a class="ref" href="fsm_1.html#T58" target="_self" title="FSM_1:th.58">Th58</a></i>;<br/>
<a NAME="E9:115"/>
( <font color="Maroon" title="c7">fsm1</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  &amp; <font color="Maroon" title="c8">fsm2</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  )
 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#T82" target="_self" title="FSM_1:th.82">Th82</a></i>;<br/>
<a NAME="E10:115"/><b>then </b><i><font color="Green" title="E93">A24</font></i>: 
( <font color="Maroon" title="c7">fsm1</font>,<font color="Maroon" title="c3">Ctfsm1</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  &amp; <font color="Maroon" title="c8">fsm2</font>,<font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a>  )
 
<b>by </b><i><a class="txt" href="fsm_1.html#E8:115"><i><font color="Green" title="E92">A23</font></i></a>, <a class="ref" href="fsm_1.html#T30" target="_self" title="FSM_1:th.30">Th30</a></i>;<br/>
<a NAME="E11:115"/><b>then </b><i><font color="Green" title="E94">A25</font></i>: 
<font color="Maroon" title="c7">fsm1</font>,<font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R4" title="FSM_1:pred.4">-are_equivalent</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:115"><i><font color="Green" title="E86">A1</font></i></a>, <a class="ref" href="fsm_1.html#T30" target="_self" title="FSM_1:th.30">Th30</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">fsm1</font> = <font color="Maroon" title="c7">fsm1</font>, <font color="Maroon" title="c18">fsm2</font> = <font color="Maroon" title="c8">fsm2</font> as  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#V5" title="FSM_1:attr.5">reduced</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> <b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#T65" target="_self" title="FSM_1:th.65">Th65</a></i>;<br/>
<a NAME="E13:115"/>
<font color="Maroon" title="c17">fsm1</font>,<font color="Maroon" title="c18">fsm2</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="txt" href="fsm_1.html#E5:115"><i><font color="Green" title="E89">A4</font></i></a>, <a class="txt" href="fsm_1.html#E7:115"><i><font color="Green" title="E91">A14</font></i></a>, <a class="txt" href="fsm_1.html#E10:115"><i><font color="Green" title="E93">A24</font></i></a>, <a class="txt" href="fsm_1.html#E11:115"><i><font color="Green" title="E94">A25</font></i></a>, <a class="ref" href="fsm_1.html#T30" target="_self" title="FSM_1:th.30">Th30</a>, <a class="ref" href="fsm_1.html#T83" target="_self" title="FSM_1:th.83">Th83</a></i>;<br/>
<a NAME="E14:115"/><b>then </b>
<font color="Maroon" title="c17">fsm1</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#T59" target="_self" title="FSM_1:th.59">Th59</a></i>;<br/>
<b>hence </b><a NAME="E15:115"/>
 <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">Ctfsm1</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">Ctfsm2</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:115"><i><font color="Green" title="E87">A2</font></i></a>, <a class="ref" href="fsm_1.html#T59" target="_self" title="FSM_1:th.59">Th59</a></i>;<br/>


</div>
