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<b>let </b><font color="Maroon">IAlph</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">OAlph</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">IAlph</font>;<br/><b>let </b><font color="Maroon">w</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font>;<br/><b>let </b><font color="Maroon">tfsm</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">IAlph</font>,<font color="Maroon">OAlph</font>;<br/><b>let </b><font color="Maroon">qa'</font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">tfsm</font>;<br/><b>let </b><font color="Maroon">qa</font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">tfsm</font>;<br/>













<b>assume </b><a NAME="E1:49"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">qa'</font> <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span>
 ;<br/>

<b>set </b><font color="Maroon">OF</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font>;<br/>
<b>set </b><font color="Maroon">asresp</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span>;<br/>
<i><font color="Green">E23</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:49_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">qa</font>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>thus </b><i><font color="Green">E38</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p4"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p4"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i/>
;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E3:49_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span></span>)</span>
 ;<br/><a NAME="E4:49_2"/><b>then </b><i><font color="Green">E40</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:49_2"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_2_2"/>
( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_2_1"><b>suppose </b></a><a NAME="E1:49_2_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">qa</font>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">qa</font>,<span class="p4">(<span class="default"><span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, </i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">qa</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:49_2"><i><font color="Green">E38</font></i></a>, </i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:49_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p4"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E2:49_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_2_2"><b>suppose </b></a><a NAME="E1:49_2_2_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:49_2_2_2"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="int_1.html#T78">INT_1:78</a></i>;<br/><a NAME="E4:49_2_2_2"/><i><font color="Green">E46</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E5:49_2_2_2"/>
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E6:49_2_2_2"/><b>then </b>
<font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E7:49_2_2_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E3:49_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E8:49_2_2_2"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T81">FINSEQ_1:81</a></i>;<br/><a NAME="E9:49_2_2_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T9">FINSEQ_2:9</a></i>;<br/><a NAME="E10:49_2_2_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">w</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E11:49_2_2_2"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="fsm_1.html#E5:49_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p4"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="txt" href="fsm_1.html#E2:49_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fsm_1.html#E3:49_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fsm_1.html#E4:49_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#T37">FINSEQ_1:37</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">w</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:49_2_2_2"><i><font color="Green">E44</font></i></a>, </i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="fsm_1.html#E1:49_2_2_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_3.html#T112">FINSEQ_3:112</a></i>
<br/>.= 
the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">qa</font>,<span class="p4">(<span class="default"><span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K2" target="_self">-admissible</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">qa</font>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="fsm_1.html#E3:49_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fsm_1.html#E3:49_2_2_2"><i><font color="Green">E45</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E13:49_2_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">qa</font>,<span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p4"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:49"/>
<font color="Maroon">qa</font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">s</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">w</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm</font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">qa</font>,<font color="Maroon">s</font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">qa'</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> </span>)</span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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