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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fsm_1.html#L1">FSM</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="fsm_2.html#V2" target="_self">accessible</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E12</font></i>: 
the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#R1">-leads_to</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="fsm_2.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:16"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:16_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E3:16_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>4</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#D2">FSM_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:16_1"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_2.html#E1:16"><i><font color="Green">E11</font></i></a>, <a class="txt" href="fsm_2.html#E3:16"><i><font color="Green">E12</font></i></a>, <a class="ref" href="fsm_1.html#D3">FSM_1:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T111">FINSEQ_3:111</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E7:16"/>
<font color="Maroon">c<sub>3</sub></font> <a href="fsm_2.html#R1" target="_self">is_accessible_via</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="fsm_2.html#E3:16"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fsm_2.html#E6:16"><i><font color="Green">E13</font></i></a>, <a class="ref" href="fsm_2.html#D2" target="_self">Def2</a></i>;<br/>


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