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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E46">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: FSM_1:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">IAlph</font>, <font color="Olive" title="b2">OAlph</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">tfsm</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> over <font color="Olive" title="b1">IAlph</font>,<font color="Olive" title="b2">OAlph</font> holds <br/> ( <font color="Olive" title="b3">tfsm</font> is  <a href="fsm_1.html#V5" title="FSM_1:attr.5">reduced</a>  iff  ex <font color="Olive" title="b4">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> over <font color="Olive" title="b1">IAlph</font>,<font color="Olive" title="b2">OAlph</font> st <font color="Olive" title="b3">tfsm</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Olive" title="b4">M</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a>  )</div></div>
