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<b>reconsider </b><font color="Maroon">n</font> =  <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<a NAME="E2:73_1_1"/>
 <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<b>then consider </b><font color="Maroon">m</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:73_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">m</font> = <font color="Maroon">m</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:73_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">m</font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">tfsm</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">tfsm</font>
 
<b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">m</font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">tfsm</font>
;<br/>

<b>thus </b><a NAME="E7:73_1_1"/>
<font color="Maroon">m</font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">tfsm</font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i>, <a class="ref" href="fsm_1.html#T10" target="_self">Th10</a></i>;<br/>


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