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<b>let </b><font color="Maroon">IAlph</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">OAlph</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">M1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</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">IAlph</font>,<font color="Maroon">OAlph</font>, <font color="Maroon">M2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</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">IAlph</font>,<font color="Maroon">OAlph</font>;<br/>





<b>thus </b><a NAME="E1:118"/>
( <font color="Maroon">M1</font>,<font color="Maroon">M2</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a>  implies <font color="Maroon">M1</font>,<font color="Maroon">M2</font> <a href="fsm_1.html#R4" target="_self">-are_equivalent</a>  )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:118"/>
<font color="Maroon">M1</font>,<font color="Maroon">M2</font> <a href="fsm_1.html#R4" target="_self">-are_equivalent</a> 
 ;<br/>

<a NAME="E3:118"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">M1</font>, <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">M2</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:118"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">M1</font>, <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">M1</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a>  &amp; <font color="Maroon">M2</font>, <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">M2</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E5:118"/><b>then </b>
<font color="Maroon">M1</font>, <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">M2</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:118"/>
<font color="Maroon">M1</font>,<font color="Maroon">M2</font> <a href="fsm_1.html#R7" target="_self">-are_isomorphic</a> 
 <b>by </b><i>, </i>;<br/>


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