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<b>let </b><font color="Maroon" title="c6">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_2.html#D6" target="_self" title="FSM_2:def.6">FSM_2:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">s</font> <a href="fsm_2.html#R2" title="FSM_2:pred.2">leads_to_final_state_of</a> <font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span><br/>

<a NAME="E1:34_1_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span>
 
<b>by </b><i><a class="ref" href="fsm_2.html#D7" target="_self" title="FSM_2:def.7">Def7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">q</font> = <font color="Maroon" title="c4">f</font> as   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">q</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_2.html#D5" target="_self" title="FSM_2:def.5">FSM_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">q</font> <a href="fsm_2.html#R1" title="FSM_2:pred.1">is_accessible_via</a> <font color="Maroon" title="c6">s</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E3:34_1_1"/>
<font color="Maroon" title="c7">q</font> <a href="fsm_2.html#R1" title="FSM_2:pred.1">is_accessible_via</a> <font color="Maroon" title="c6">s</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon" title="c8">w</font> =  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">I</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_2.html#D2" target="_self" title="FSM_2:def.2">FSM_2:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span>,<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">w</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c7">q</font></span><br/>

<a NAME="E1:34_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E2:34_1_1_1"/><b>then </b>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:34_1_1_1"/>
<span class="p1">(<span class="default"><a href="fsm_2.html#NK1" title="FSM_2:NK.1">GEN</a> <span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">w</font></span>)</span>,the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">s</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c8">w</font></span>)</span></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="c7">q</font>
 <b>by </b><i><a class="ref" href="fsm_2.html#T17" target="_self" title="FSM_2:th.17">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D3" title="FSM_1:def.3">FSM_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<a NAME="E4:34_1_1"/>
the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="fsm_2.html#D7" target="_self" title="FSM_2:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E5:34_1_1"/>
<font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="fsm_2.html#K1" title="FSM_2:func.1">-TwoStatesMooreSM</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">o</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
