<?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>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<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#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <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#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>assume </b><a NAME="E1:63"/>
 <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<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#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:63"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <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#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<a NAME="E3:63"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<a NAME="E4:63"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>assume </b><a NAME="E1:63_1"/>
 <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:63_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#T8" target="_self">Th8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:63_1_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><a NAME="E3:63_1_1_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/><b>consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:63_1_1_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:63_1_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_1"><i><font color="Green">E50</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:63_1_1_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E3:63_1_1_1"><i><font color="Green">E49</font></i></a></i>;<br/><a NAME="E3:63_1_1_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="fsm_1.html#E1:63_1_1_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/><a NAME="E4:63_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E5:63_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#T43" target="_self">Th43</a></i>;<br/><a NAME="E6:63_1_1_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E7:63_1_1_1_1_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:63_1_1_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><a NAME="E4:63_1_1_1_1"/><i><font color="Green">E52</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63_1_1_1_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/><a NAME="E5:63_1_1_1_1"/><i><font color="Green">E53</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:63_1_1_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63"><i><font color="Green">E44</font></i></a>, <a class="txt" href="fsm_1.html#E4:63_1_1_1_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E7:63_1_1_1_1"/><i><font color="Green">E55</font></i>: 
1 <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="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E8:63_1_1_1_1"/><b>then </b><i><font color="Green">E56</font></i>: 
1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:63_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>21</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>22</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_1_1_1_1_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>set </b><font color="Maroon">c<sub>24</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><a NAME="E2:63_1_1_1_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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="xcmplx_0.html#K6">-</a> 1
 ;<br/><a NAME="E3:63_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E6:63_1_1_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="fsm_1.html#E7:63_1_1_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><a NAME="E4:63_1_1_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E5:63_1_1_1_1_2"/>
<font color="Maroon">c<sub>22</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fsm_1.html#E1:63_1_1_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/></div><b>end;</b></div><a NAME="E10:63_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_1_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="fsm_1.html#E8:63_1_1_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><a NAME="E11:63_1_1_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E12:63_1_1_1_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/></div><b>end;</b></div><a NAME="E8:63_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>hence </b><a NAME="E9:63_1_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:63_1_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>15</sub></font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><b>consider </b><font color="Maroon">c<sub>17</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:63_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63_1_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1"><i><font color="Green">E49</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:63_1_1_2_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1"><i><font color="Green">E49</font></i></a></i>;<br/><a NAME="E3:63_1_1_2_1"/><i><font color="Green">E51</font></i>: 
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fsm_1.html#E1:63_1_1_2_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/><a NAME="E4:63_1_1_2_1"/><i><font color="Green">E52</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E5:63_1_1_2_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63"><i><font color="Green">E44</font></i></a>, <a class="txt" href="fsm_1.html#E3:63_1_1_2_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E6:63_1_1_2_1"/><i><font color="Green">E54</font></i>: 
1 <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="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E7:63_1_1_2_1"/><b>then </b><i><font color="Green">E55</font></i>: 
1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_2_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>21</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>22</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:63_1_1_2_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><b>set </b><font color="Maroon">c<sub>24</sub></font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/><a NAME="E2:63_1_1_2_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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="xcmplx_0.html#K6">-</a> 1
 ;<br/><a NAME="E3:63_1_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1_2_1"><i><font color="Green">E53</font></i></a>, <a class="txt" href="fsm_1.html#E6:63_1_1_2_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><a NAME="E4:63_1_1_2_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span>,<span class="p2">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E5:63_1_1_2_1_1"/>
<font color="Maroon">c<sub>22</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fsm_1.html#E1:63_1_1_2_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/></div><b>end;</b></div><a NAME="E9:63_1_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E4:63_1_1_2_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fsm_1.html#E7:63_1_1_2_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="fsm_1.html#T44" target="_self">Th44</a></i>;<br/><a NAME="E10:63_1_1_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E11:63_1_1_2_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:63_1_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>19</sub></font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> ;<br/><a NAME="E4:63_1_1_2"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E2:63_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/><a NAME="E5:63_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E6:63_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#R6" target="_self">-equivalent</a> <font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#T43" target="_self">Th43</a></i>;<br/><a NAME="E7:63_1_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>18</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E8:63_1_1_2"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:63_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/></div><b>end;</b></div><a NAME="E8:63_1_1"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><b>hence </b><a NAME="E9:63_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:63_1"/>
 <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_1.html#K6" target="_self">-eq_states_EqR</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E5:63"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="fsm_1.html#E3:63"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fsm_1.html#E4:63"><i><font color="Green">E46</font></i></a>);</i><br/>


</div>
