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<b>let </b><font color="Maroon" title="c1">IAlph</font>, <font color="Maroon" title="c2">OAlph</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">tfsm</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font>;<br/><b>let </b><font color="Maroon" title="c4">q</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font>;<br/>







<b>set </b><font color="Maroon" title="c5">0e</font> = 0 <a href="fsm_1.html#K6" title="FSM_1:func.6">-eq_states_EqR</a> <font color="Maroon" title="c3">tfsm</font>;<br/>
<b>set </b><font color="Maroon" title="c6">S</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>thus </b><a NAME="E1:64_1"/>
( <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default">0 <a href="fsm_1.html#K6" title="FSM_1:func.6">-eq_states_EqR</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c4">q</font> implies <font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font> )
 ;<br/><b>assume </b><a NAME="E2:64_1"/>
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c8">z'</font> = <font color="Maroon" title="c7">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font> ;<br/><a NAME="E4:64_1"/>
0 <a href="fsm_1.html#R6" title="FSM_1:pred.6">-equivalent</a> <font color="Maroon" title="c8">z'</font>,<font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="ref" href="fsm_1.html#T42" target="_self" title="FSM_1:th.42">Th42</a></i>;<br/><a NAME="E5:64_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">z</font>,<font color="Maroon" title="c4">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 0 <a href="fsm_1.html#K6" title="FSM_1:func.6">-eq_states_EqR</a> <font color="Maroon" title="c3">tfsm</font>
 <b>by </b><i><a class="ref" href="fsm_1.html#D12" target="_self" title="FSM_1:def.12">Def12</a></i>;<br/><b>hence </b><a NAME="E6:64_1"/>
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default">0 <a href="fsm_1.html#K6" title="FSM_1:func.6">-eq_states_EqR</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T27" title="EQREL_1:th.27">EQREL_1:27</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:64"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default">0 <a href="fsm_1.html#K6" title="FSM_1:func.6">-eq_states_EqR</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>,<font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>;<br/>


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