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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">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> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font><br/> for <font color="Olive" title="b2">CRtfsm2</font>, <font color="Olive" title="b3">CRtfsm1</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#V5" title="FSM_1:attr.5">reduced</a>   <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</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/> for <font color="Olive" title="b4">q1u</font>, <font color="Olive" title="b5">q2u</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">tfsm</font><br/> for <font color="Olive" title="b6">crq21</font>, <font color="Olive" title="b7">crq22</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b2">CRtfsm2</font>  st <font color="Olive" title="b6">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q1u</font> &amp; <font color="Olive" title="b7">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q2u</font> &amp; <font color="Olive" title="b1">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Olive" title="b2">CRtfsm2</font> &amp; not <font color="Olive" title="b6">crq21</font>,<font color="Olive" title="b7">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  holds <br/> not <font color="Olive" title="b4">q1u</font>,<font color="Olive" title="b5">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">tfsm</font> be  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> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">CRtfsm2</font>, <font color="Olive" title="b2">CRtfsm1</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#V5" title="FSM_1:attr.5">reduced</a>   <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</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/> for <font color="Olive" title="b3">q1u</font>, <font color="Olive" title="b4">q2u</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font><br/> for <font color="Olive" title="b5">crq21</font>, <font color="Olive" title="b6">crq22</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">CRtfsm2</font>  st <font color="Olive" title="b5">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q1u</font> &amp; <font color="Olive" title="b6">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q2u</font> &amp; <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Olive" title="b1">CRtfsm2</font> &amp; not <font color="Olive" title="b5">crq21</font>,<font color="Olive" title="b6">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  holds <br/> not <font color="Olive" title="b3">q1u</font>,<font color="Olive" title="b4">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">CRtfsm2</font>, <font color="Maroon" title="c5">CRtfsm1</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#V5" title="FSM_1:attr.5">reduced</a>   <a href="fsm_1.html#V7" title="FSM_1:attr.7">connected</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">q1u</font>, <font color="Olive" title="b2">q2u</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font><br/> for <font color="Olive" title="b3">crq21</font>, <font color="Olive" title="b4">crq22</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c4">CRtfsm2</font>  st <font color="Olive" title="b3">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q1u</font> &amp; <font color="Olive" title="b4">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q2u</font> &amp; <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c4">CRtfsm2</font> &amp; not <font color="Olive" title="b3">crq21</font>,<font color="Olive" title="b4">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  holds <br/> not <font color="Olive" title="b1">q1u</font>,<font color="Olive" title="b2">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">q1u</font>, <font color="Maroon" title="c7">q2u</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">tfsm</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">crq21</font>, <font color="Olive" title="b2">crq22</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c4">CRtfsm2</font>  st <font color="Olive" title="b1">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1u</font> &amp; <font color="Olive" title="b2">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">q2u</font> &amp; <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c4">CRtfsm2</font> &amp; not <font color="Olive" title="b1">crq21</font>,<font color="Olive" title="b2">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  holds <br/> not <font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c7">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c8">crq21</font>, <font color="Maroon" title="c9">crq22</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c4">CRtfsm2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1u</font> &amp; <font color="Maroon" title="c9">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">q2u</font> &amp; <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c4">CRtfsm2</font> &amp; not <font color="Maroon" title="c8">crq21</font>,<font color="Maroon" title="c9">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  implies  not <font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c7">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/>















<span class="kw">set </span><font color="Maroon" title="c10">rtfsm1</font> = <font color="Maroon" title="c5">CRtfsm1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">rtfsm2</font> = <font color="Maroon" title="c4">CRtfsm2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">q1</font> = <font color="Maroon" title="c8">crq21</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">q2</font> = <font color="Maroon" title="c9">crq22</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:114"/><span class="lab"><font color="Green" title="E78">A1</font></span>: 
<font color="Maroon" title="c8">crq21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1u</font>
 <span class="kw">and </span><br/><a NAME="E2:114"/><span class="lab"><font color="Green" title="E79">A2</font></span>: 
<font color="Maroon" title="c9">crq22</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">q2u</font>
 <span class="kw">and </span><br/><a NAME="E3:114"/><span class="lab"><font color="Green" title="E80">A3</font></span>: 
<font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c4">CRtfsm2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">crq21</font>,<font color="Maroon" title="c9">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  or  not <font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c7">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E4:114"/>
not <font color="Maroon" title="c8">crq21</font>,<font color="Maroon" title="c9">crq22</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c7">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><span class="kw"> such that </span><br/><a NAME="E6:114"/><span class="lab"><font color="Green" title="E81">A4</font></span>: 
<font color="Maroon" title="c8">crq21</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">crq22</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</a></span>;<br/>
<a NAME="E7:114"/>
<font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">crq21</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:114"><span class="lab"><font color="Green" title="E78">A1</font></span></a>, <a class="txt" href="#E3:114"><span class="lab"><font color="Green" title="E80">A3</font></span></a>, <a class="ref" href="fsm_1.html#T74" target="_self" title="FSM_1:th.74">Th74</a></span>;<br/>
<a NAME="E8:114"/><span class="kw">then </span>
<font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q2u</font>,<font color="Maroon" title="c14">w</font> <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:114"><span class="lab"><font color="Green" title="E79">A2</font></span></a>, <a class="txt" href="#E3:114"><span class="lab"><font color="Green" title="E80">A3</font></span></a>, <a class="txt" href="#E6:114"><span class="lab"><font color="Green" title="E81">A4</font></span></a>, <a class="ref" href="fsm_1.html#T74" target="_self" title="FSM_1:th.74">Th74</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:114"/>
not <font color="Maroon" title="c6">q1u</font>,<font color="Maroon" title="c7">q2u</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D10" target="_self" title="FSM_1:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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