<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:64"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</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>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E2:64"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:64"/><i><font color="Green">E47</font></i>: 
<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>4</sub></font> <a href="hidden.html#R1">=</a> <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>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:64"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:64"><i><font color="Green">E46</font></i></a>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E6:64"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K7" target="_self">-eq_states_partition</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <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>4</sub></font>
 
<b>by </b><i><a class="txt" href="fsm_1.html#E3:64"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fsm_1.html#E5:64"><i><font color="Green">E48</font></i></a>, <a class="ref" href="fsm_1.html#T46" target="_self">Th46</a></i>;<br/>
<a NAME="E7:64"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="fsm_1.html#E2:64"><i><font color="Green">E46</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E9:64"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>thus </b><a NAME="E10:64"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:64"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fsm_1.html#E3:64"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fsm_1.html#E6:64"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fsm_1.html#E9:64"><i><font color="Green">E50</font></i></a>, <a class="ref" href="fsm_1.html#T46" target="_self">Th46</a></i>;<br/>


</div>
