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<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">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>;<br/><b>let </b><font color="Maroon" title="c5">tfsm</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</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>let </b><font color="Maroon" title="c6">q1t</font>, <font color="Maroon" title="c7">q2t</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c5">tfsm</font>;<br/>













<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c6">q1t</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="c7">q2t</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c8">q1w1</font> = <font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<b>set </b><font color="Maroon" title="c9">q2w2</font> = <font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<b>set </b><font color="Maroon" title="c10">q1w1w2</font> = <font color="Maroon" title="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> ;<br/>
<b>set </b><font color="Maroon" title="c11">Dq1w1w2a</font> =  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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>;<br/>
<b>set </b><font color="Maroon" title="c12">OF</font> = the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font>;<br/>
<i><font color="Green" title="E27">A2</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> = 
 <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>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</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="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>
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
<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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c13">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:37_2"/><i><font color="Green" title="E28">A3</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> )
 ;<br/><a NAME="E2:37_2"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E3:37_2"/><i><font color="Green" title="E30">A5</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="c6">q1t</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
 <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="E4:37_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</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>  <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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span></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="E5:37_2"/><b>then </b>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</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>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <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="E6:37_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="c3">w1</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</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#T5" title="FINSEQ_1:th.5">FINSEQ_1:5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c14">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E8:37_2"/><i><font color="Green" title="E31">A6</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="c6">q1t</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> <font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</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> <font color="Maroon" title="c14">m</font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T113" title="FINSEQ_3:th.113">FINSEQ_3:113</a></i>;<br/><a NAME="E9:37_2"/><i><font color="Green" title="E32">A7</font></i>: 
<font color="Maroon" title="c14">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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
 <b>by </b><i><a class="txt" href="fsm_1.html#E8:37_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></i>;<br/><a NAME="E10:37_2"/><i><font color="Green" title="E33">A8</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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_2_1"/>
( ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> ) or ( <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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_1"><b>suppose </b></a><a NAME="E1:37_2_1_1"/><i><font color="Green" title="E34">A9</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> )
 ;<br/><div class="add"><a NAME="E2:37_2_1_1"/><b>then </b><i><font color="Green" title="E35">A10</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font> )
 <b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><a NAME="E3:37_2_1_1"/><b>then </b><i><font color="Green" title="E36">A11</font></i>: 
<font color="Maroon" title="c13">k</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>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:37_2_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><a NAME="E5:37_2_1_1"/><b>then </b><i><font color="Green" title="E37">A12</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:37_2_1_1"/><i><font color="Green" title="E38">A13</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2_1_1"><i><font color="Green" title="E34">A9</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E7:37_2_1_1"/><i><font color="Green" title="E39">A14</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:37_2_1_1"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:37_2_1_1"/><i><font color="Green" title="E40">A15</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E8:37_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="fsm_1.html#E9:37_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="fsm_1.html#E2:37_2_1_1"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> = 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<span class="p4">(<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> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E5:37_2_1_1"><i><font color="Green" title="E37">A12</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<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>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="fsm_1.html#T23" target="_self" title="FSM_1:th.23">Th23</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<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>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E8:37_2_1_1"><i><font color="Green" title="E40">A15</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<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>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:37_2_1_1"><i><font color="Green" title="E36">A11</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</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> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:37_2"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="fsm_1.html#E3:37_2"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="fsm_1.html#E7:37_2_1_1"><i><font color="Green" title="E39">A14</font></i></a>, <a class="ref" href="finseq_3.html#T119" title="FINSEQ_3:th.119">FINSEQ_3:119</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:37_2_1_1"><i><font color="Green" title="E36">A11</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E6:37_2_1_1"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_2_1_2"><b>suppose </b></a><a NAME="E1:37_2_1_2"/><i><font color="Green" title="E34">A16</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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> )
 ;<br/><div class="add"><a NAME="E2:37_2_1_2"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</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> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><a NAME="E3:37_2_1_2"/><b>then </b><i><font color="Green" title="E35">A17</font></i>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><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>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><i><font color="Green" title="E36">A18</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> = 
 <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>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</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="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>
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
<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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
<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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
;<br/><a NAME="E5:37_2_1_2"/><b>then </b><i><font color="Green" title="E37">A19</font></i>: 
<font color="Maroon" title="c13">k</font> <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">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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>
 <b>by </b><i><a class="txt" href="fsm_1.html#E8:37_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="fsm_1.html#E9:37_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="fsm_1.html#E10:37_2"><i><font color="Green" title="E33">A8</font></i></a>, <a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><a NAME="E6:37_2_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">w2</font> <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="c4">w2</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="E7:37_2_1_2"/><b>then </b>
<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"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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> <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">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c4">w2</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E8:37_2_1_2"/><b>then </b>
<font color="Maroon" title="c13">k</font> <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">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c4">w2</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#E5:37_2_1_2"><i><font color="Green" title="E37">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E9:37_2_1_2"/><b>then </b><i><font color="Green" title="E38">A20</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"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <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">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</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#E8:37_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="fsm_1.html#E9:37_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></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#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><i><font color="Green" title="E39">A21</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="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> = 
 <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>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</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="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>
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
;<br/><a NAME="E11:37_2_1_2"/><b>then </b><i><font color="Green" title="E40">A22</font></i>: 
( <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 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> &amp; <font color="Maroon" title="c13">k</font> <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="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> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><i><font color="Green" title="E41">A23</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> = 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<span class="p4">(<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> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:37_2_1_2"><i><font color="Green" title="E35">A17</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<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>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:37"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="fsm_1.html#T23" target="_self" title="FSM_1:th.23">Th23</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</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"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span>,<span class="p0">(<span class="default"><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>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<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> <font color="Maroon" title="c13">k</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E9:37_2_1_2"><i><font color="Green" title="E38">A20</font></i></a>, <a class="ref" href="finseq_1.html#T36" title="FINSEQ_1:th.36">FINSEQ_1:36</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</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"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<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>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<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>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E8:37_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="fsm_1.html#E9:37_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="fsm_1.html#E11:37_2_1_2"><i><font color="Green" title="E40">A22</font></i></a>, <a class="ref" href="finseq_1.html#T36" title="FINSEQ_1:th.36">FINSEQ_1:36</a></i>
;<br/><a NAME="E13:37_2_1_2"/><i><font color="Green" title="E42">A24</font></i>: 
<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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c15">p</font> = <font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E15:37_2_1_2"/>
<font color="Maroon" title="c13">k</font> <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">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></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>
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="txt" href="fsm_1.html#E10:37_2_1_2"><i><font color="Green" title="E39">A21</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>;<br/><a NAME="E16:37_2_1_2"/><b>then </b>
<font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<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>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</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"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E17:37_2_1_2"/><b>then </b><i><font color="Green" title="E43">A25</font></i>: 
<font color="Maroon" title="c15">p</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="c4">w2</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E13:37_2_1_2"><i><font color="Green" title="E42">A24</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">p</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:37_2_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="txt" href="fsm_1.html#E4:37_2_1_2"><i><font color="Green" title="E36">A18</font></i></a>, <a class="ref" href="finseq_1.html#T36" title="FINSEQ_1:th.36">FINSEQ_1:36</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">p</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">p</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E17:37_2_1_2"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</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"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<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>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p5">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">tfsm</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</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"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<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>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<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>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></i>
;<br/><b>hence </b><a NAME="E19:37_2_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</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#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">k</font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E12:37_2_1_2"><i><font color="Green" title="E41">A23</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:37"/>
<font color="Maroon" title="c6">q1t</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#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1t</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">q2t</font>,<font color="Maroon" title="c4">w2</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:37"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</a></i>;<br/>


</div>
