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<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> as   <a href="nat_1.html#NM1">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">c<sub>3</sub></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">c<sub>5</sub></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">E51</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E5:73_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:73_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="fsm_1.html#T52" target="_self">Th52</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E6:73_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">c<sub>3</sub></font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:73_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="fsm_1.html#T54" target="_self">Th54</a></i>;<br/>


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