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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="fsm_1.html#V5" target="_self">reduced</a> <a href="fsm_1.html#V7" target="_self">connected</a>  <a href="fsm_1.html#L2" target="_self">Mealy-FSM</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="fsm_1.html#NM1">State</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>















<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>8</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>9</sub></font>;<br/>
<b>assume </b><a NAME="E1:109"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="fsm_1.html#R4" target="_self">-are_equivalent</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="fsm_1.html#K13" target="_self">-Mealy_union</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:109"/>
not <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:109"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E5:109"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:109"><i><font color="Green">E79</font></i></a>, <a class="ref" href="fsm_1.html#T72" target="_self">Th72</a></i>;<br/>
<a NAME="E6:109"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 
<b>by </b><i><a class="txt" href="fsm_1.html#E1:109"><i><font color="Green">E79</font></i></a>, <a class="txt" href="fsm_1.html#E4:109"><i><font color="Green">E80</font></i></a>, <a class="ref" href="fsm_1.html#T72" target="_self">Th72</a></i>;<br/>
<b>hence </b><a NAME="E7:109"/>
not <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="ref" href="fsm_1.html#D10" target="_self">Def10</a></i>;<br/>


</div>
