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<span class="kw">let </span><font color="Maroon" title="c1">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">fsm</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L1" title="FSM_1:struct.1">FSM</a> of <font color="Maroon" title="c1">IAlph</font><br/>  for <font color="Olive" title="b2">w1</font>, <font color="Olive" title="b3">w2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><br/>  for <font color="Olive" title="b4">q1</font>, <font color="Olive" title="b5">q2</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">fsm</font>  st <font color="Olive" title="b4">q1</font>,<font color="Olive" title="b2">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b5">q2</font> holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b4">q1</font>,<span class="p2">(<span class="default"><font color="Olive" title="b2">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">w2</font></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> <font color="Olive" title="b2">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">fsm</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L1" title="FSM_1:struct.1">FSM</a> of <font color="Maroon" title="c1">IAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">w1</font>, <font color="Olive" title="b2">w2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><br/>  for <font color="Olive" title="b3">q1</font>, <font color="Olive" title="b4">q2</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c2">fsm</font>  st <font color="Olive" title="b3">q1</font>,<font color="Olive" title="b1">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b4">q2</font> holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b3">q1</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">w2</font></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> <font color="Olive" title="b1">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">w1</font>, <font color="Maroon" title="c4">w2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">q1</font>, <font color="Olive" title="b2">q2</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c2">fsm</font>  st <font color="Olive" title="b1">q1</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b2">q2</font> holds <br/><span class="p1">(<span class="default">(<font color="Olive" title="b1">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">q1</font>, <font color="Maroon" title="c6">q2</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c2">fsm</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c6">q2</font> implies <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font> )</span><br/>











<span class="kw">assume </span><a NAME="E1:14"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c6">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">q1w1</font> = (<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">q1w</font> = (<font color="Maroon" title="c5">q1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:14_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1"><span class="kw">suppose </span></a><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font></span><br/><div class="add"><a NAME="E2:14_1_1"/>
( <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</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> <font color="Maroon" title="c5">q1</font> &amp; <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a>, <a class="ref" href="fsm_1.html#D3" target="_self" title="FSM_1:def.3">Def3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1"/>
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_2"><span class="kw">suppose </span></a><a NAME="E1:14_1_2"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q2</font></span><br/><div class="add"><a NAME="E2:14_1_2"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E3:14_1_2"/>
<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/><a NAME="E4:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A5</font></span>: 
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> <font color="Maroon" title="c3">w1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">w1k</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="c10">qw1k</font>, <font color="Maroon" title="c11">qw1k1</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c2">fsm</font><span class="kw"> such that </span><br/><a NAME="E6:14_1_2"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
<font color="Maroon" title="c9">w1k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.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="c3">w1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:14_1_2"/><span class="lab"><font color="Green" title="E15">A7</font></span>: 
<font color="Maroon" title="c10">qw1k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:14_1_2"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
<font color="Maroon" title="c11">qw1k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<font color="Maroon" title="c3">w1</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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E9:14_1_2"/><span class="lab"><font color="Green" title="E17">A9</font></span>: 
<font color="Maroon" title="c9">w1k</font> <a href="fsm_1.html#K1" title="FSM_1:func.1">-succ_of</a> <font color="Maroon" title="c10">qw1k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">qw1k1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E10:14_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">w2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T22" title="FINSEQ_1:th.22">FINSEQ_1:22</a></span>;<br/><a NAME="E11:14_1_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">wk</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="c13">qwk</font>, <font color="Maroon" title="c14">qwk1</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c2">fsm</font><span class="kw"> such that </span><br/><a NAME="E13:14_1_2"/><span class="lab"><font color="Green" title="E18">A10</font></span>: 
<font color="Maroon" title="c12">wk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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="c3">w1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E14:14_1_2"/><span class="lab"><font color="Green" title="E19">A11</font></span>: 
( <font color="Maroon" title="c13">qwk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font></span>)</span> &amp; <font color="Maroon" title="c14">qwk1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c12">wk</font> <a href="fsm_1.html#K1" title="FSM_1:func.1">-succ_of</a> <font color="Maroon" title="c13">qwk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">qwk1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>;<br/><a NAME="E15:14_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</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="c3">w1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></span>;<br/><a NAME="E16:14_1_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</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="c3">w1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><a NAME="E17:14_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">wk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_2"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="txt" href="#E6:14_1_2"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default">(<font color="Maroon" title="c5">q1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></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> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<font color="Maroon" title="c11">qw1k1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E14:14_1_2"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E7:14_1_2"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E9:14_1_2"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="fsm_1.html#T5" target="_self" title="FSM_1:th.5">Th20</a></span>
<br/>.= 
<font color="Maroon" title="c6">q2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E8:14_1_2"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="fsm_1.html#T4" target="_self" title="FSM_1:th.4">Th19</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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