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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">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">qb</font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">tfsm</font>;<br/><b>let </b><font color="Maroon">qc</font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">tfsm</font>;<br/><b>let </b><font color="Maroon">k</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>













<b>assume </b><a NAME="E1:55"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">k</font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">qa</font>,<font color="Maroon">qb</font> &amp; <font color="Maroon">k</font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">qb</font>,<font color="Maroon">qc</font> )
 ;<br/>

<b>thus </b><a NAME="E2:55"/>
<font color="Maroon">k</font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">qa</font>,<font color="Maroon">qc</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">w</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D11" target="_self">FSM_1:def 11</a><br/>

<b>assume </b><a NAME="E1:55_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">w</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 ;<br/>

<a NAME="E2:55_1"/><b>then </b>
( <font color="Maroon">qa</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">qb</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a>  &amp; <font color="Maroon">qb</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">qc</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a>  )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:55_1"/>
<font color="Maroon">qa</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">qc</font>,<font color="Maroon">w</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 ;<br/>


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


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