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<b>reconsider </b><font color="Maroon" title="c4">n</font> =  <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="c3">tfsm</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E2:70_1_1"/>
 <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="c3">tfsm</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:70_1_1"/><i><font color="Green" title="E50">A1</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">m</font> = <font color="Maroon" title="c5">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:70_1_1"/><i><font color="Green" title="E51">A2</font></i>: 
<font color="Maroon" title="c6">m</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">m</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="c3">tfsm</font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E4:70_1_1"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="fsm_1.html#T52" target="_self" title="FSM_1:th.52">Th52</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">m</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c3">tfsm</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">m</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c3">tfsm</font> is <a href="fsm_1.html#V4" title="FSM_1:attr.4">final</a></span><br/>

<b>thus </b><a NAME="E7:70_1_1"/>
<font color="Maroon" title="c6">m</font> <a href="fsm_1.html#K7" title="FSM_1:func.7">-eq_states_partition</a> <font color="Maroon" title="c3">tfsm</font> is <a href="fsm_1.html#V4" title="FSM_1:attr.4">final</a>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:70_1_1"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="fsm_1.html#T54" target="_self" title="FSM_1:th.54">Th54</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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