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<b>let </b><font color="Maroon" title="c1">n</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c2">IAlph</font>, <font color="Maroon" title="c3">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="c4">tfsm</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c2">IAlph</font>,<font color="Maroon" title="c3">OAlph</font>;<br/>







<b>assume </b><a NAME="E1:70"/><i><font color="Green" title="E51">A1</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">tfsm</font>
 ;<br/>

<b>take </b>
<font color="Maroon" title="c1">n</font>
;<br/>

<b>thus </b><a NAME="E2:70"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 ;<br/>

<a NAME="E3:70"/>
<font color="Maroon" title="c1">n</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c4">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c4">tfsm</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:70"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="fsm_1.html#T52" target="_self" title="FSM_1:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E4:70"/>
<font color="Maroon" title="c1">n</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c4">tfsm</font> is <a href="fsm_1.html#V4" title="FSM_1:attr.4">final</a>
 <b>by </b><i><a class="ref" href="fsm_1.html#T54" target="_self" title="FSM_1:th.54">Th54</a></i>;<br/>


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