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<div class="add">

<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">tfsm</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">IAlph</font>,<font color="Maroon">OAlph</font>;<br/><b>let </b><font color="Maroon">CRtfsm1</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>let </b><font color="Maroon">CRtfsm2</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>set </b><font color="Maroon">rtfsm1</font> = <font color="Maroon">CRtfsm1</font>;<br/>
<b>set </b><font color="Maroon">rtfsm2</font> = <font color="Maroon">CRtfsm2</font>;<br/>
<b>assume </b><a NAME="E1:113"/><i><font color="Green">E22</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="subset_1.html#R1">misses</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> &amp; <font color="Maroon">CRtfsm1</font>,<font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#R4" target="_self">-are_equivalent</a>  &amp; <font color="Maroon">tfsm</font> <a href="hidden.html#R1">=</a> <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K13" target="_self">-Mealy_union</a> <font color="Maroon">CRtfsm2</font> )
 ;<br/>

<b>assume </b><a NAME="E2:113"/>
 ex <font color="Olive">Q</font> being  <a href="fsm_1.html#NM1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span> st <br/>for <font color="Olive">q1</font>, <font color="Olive">q2</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">Q</font>  holds <br/>(  not <font color="Olive">q1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Olive">q2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  ex <font color="Olive">q</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">Q</font> st <br/>( not <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">q1</font> &amp; not <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">q2</font> ) )
 ;<br/>

<b>then consider </b><font color="Maroon">Q</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span><b> such that </b><br/><a NAME="E4:113"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">q1</font>, <font color="Olive">q2</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font>  holds <br/>(  not <font color="Olive">q1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Olive">q2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  ex <font color="Olive">q</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> st <br/>( not <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">q1</font> &amp; not <font color="Olive">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">q2</font> ) )
 ;<br/>
<a NAME="E5:113"/><i><font color="Green">E38</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>set </b><font color="Maroon">rtfsm</font> =  <a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font>;<br/>
<b>set </b><font color="Maroon">Srtfsm1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>;<br/>
<b>set </b><font color="Maroon">ISrtfsm1</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font>;<br/>
<b>set </b><font color="Maroon">Srtfsm2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>;<br/>
<b>set </b><font color="Maroon">ISrtfsm2</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font>;<br/>
<b>set </b><font color="Maroon">Stfsm</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font>;<br/>
<b>set </b><font color="Maroon">Srtfsm</font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>;<br/>
<a NAME="E6:113"/><i><font color="Green">E39</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">Q</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E8:113"/>
<font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>
 
;<br/>
<a NAME="E9:113"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:113"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">q</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font><b> such that </b><br/><a NAME="E12:113"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
 <a href="setfam_1.html#K5">union</a> <span class="p1">(<span class="default"><a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font>
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
<b>by </b><i>, </i>
;<br/>
<a NAME="E14:113"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2"/>
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1"><b>suppose </b></a><a NAME="E1:113_2_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">Q'</font> = <font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E46</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <b>by </b><i/>;<br/><a NAME="E3:113_2_1_1"/>
<font color="Maroon">q</font> is <a href="fsm_1.html#V6" target="_self">accessible</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">w</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font><b> such that </b><br/><a NAME="E5:113_2_1_1"/><i><font color="Green">E79</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font>,<font color="Maroon">w</font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/><b>set </b><font color="Maroon">adl</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font>;<br/><div><i><font color="Green">E81</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1_1"/><i><font color="Green">E82</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><a NAME="E2:113_2_1_1_1"/>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:113_2_1_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_1_2"/><i><font color="Green">E83</font></i>: 
not the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><a NAME="E2:113_2_1_1_2"/><i><font color="Green">E84</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">adl</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_1_2"><i><font color="Green">E83</font></i></a>, , </i>;<br/><a NAME="E5:113_2_1_1_2"/><i><font color="Green">E86</font></i>: 
 <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i/>;<br/><a NAME="E6:113_2_1_1_2"/>
for <font color="Olive">Y</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>  holds <br/>(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> or  not <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:113_2_1_1_2_1"/>
 ex <font color="Olive">Y</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span> st <br/>( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> &amp; <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">Y</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span><b> such that </b><br/><a NAME="E3:113_2_1_1_2_1"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <b>by </b><i><a class="txt" href="fsm_1.html#E5:113_2_1_1_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">Q</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/>
<a NAME="E6:113_2_1_1_2_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>
 
;<br/>
<a NAME="E7:113_2_1_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:113_2_1_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E9:113_2_1_1_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:113_2_1_1_2"/><b>then </b>
not <font color="Maroon">q</font>,<font color="Maroon">adl</font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E5:113_2_1_1_2"><i><font color="Green">E86</font></i></a>, , </i>;<br/><b>then consider </b><font color="Maroon">dseq</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font><b> such that </b><br/><a NAME="E9:113_2_1_1_2"/><i><font color="Green">E180</font></i>: 
<font color="Maroon">q</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">adl</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">adl2</font> = <font color="Maroon">adl</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> ;<br/><b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> ;<br/><a NAME="E12:113_2_1_1_2"/><i><font color="Green">E181</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font>,<font color="Maroon">w</font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">adl2</font>
 <b>by </b><i/>;<br/><a NAME="E13:113_2_1_1_2"/>
<font color="Maroon">q</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_1_2"><i><font color="Green">E83</font></i></a>, </i>;<br/><a NAME="E14:113_2_1_1_2"/><b>then </b>
<font color="Maroon">q1</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">adl2</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_1_2"><i><font color="Green">E83</font></i></a>, , </i>;<br/><a NAME="E15:113_2_1_1_2"/><b>then </b>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font>,<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">dseq</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font>,<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">dseq</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E16:113_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="fsm_1.html#E1:113_2_1_1_2"><i><font color="Green">E83</font></i></a>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:113_2_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2"/><i><font color="Green">E182</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2"/><i><font color="Green">E183</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">Q</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">Q'</font> = <font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font><b> such that </b><br/><a NAME="E6:113_2_1_2"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_1_2"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">Q'</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_1"/><i><font color="Green">E287</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:113_2_1_2_1_1"/>
(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:113_2_1_2_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2"/><i><font color="Green">E288</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">Q''</font> = <font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E289</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2_1_2_1"/><i><font color="Green">E473</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2_1_2_1"/><i><font color="Green">E474</font></i>: 
for <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font>  holds <br/>( <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> or <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">z</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font><b> such that </b><a NAME="E1:113_2_1_2_1_2_1_1"/><i><font color="Green">E475</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> )
 ;<br/>

<a NAME="E2:113_2_1_2_1_2_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E3:113_2_1_2_1_2_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_1"/>
(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  ex <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> st <br/>( <font color="Olive">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Olive">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_1_2_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_1_2_1_2_2"/><i><font color="Green">E476</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_1_2_1_2_2"/><i><font color="Green">E477</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q'</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">Q'</font> = <font color="Maroon">Q'</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">Q''</font> = <font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font><b> such that </b><br/><a NAME="E6:113_2_1_2_1_2_2"/><i><font color="Green">E478</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q''</font>
 <b>by </b><i>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_1_2_1_2_2"/><i><font color="Green">E479</font></i>: 
<font color="Maroon">Q''</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_1_2_1_2_2_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2_2_1_1"/><i><font color="Green">E480</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>
 ;<br/><div class="add"><a NAME="E2:113_2_1_2_1_2_2_1_1"/><i><font color="Green">E481</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self">Def2</a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_2_1_1"/>
(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_2_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="fsm_1.html#D2" target="_self">Def2</a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_1_2_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_1_2_1_2_2_1_2"/><i><font color="Green">E482</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E3:113_2_1_2_1_2_2_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_1_2_1_2_2_1_2"/>
(  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:113_2_1_2_1_2_2_1_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_1_2_1_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2"><b>suppose </b></a><a NAME="E1:113_2_2"/><i><font color="Green">E483</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">Q'</font> = <font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E484</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1"/><i><font color="Green">E485</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> <b>by </b><i/>;<br/><a NAME="E3:113_2_2_1"/>
<font color="Maroon">q</font> is <a href="fsm_1.html#V6" target="_self">accessible</a>
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">w</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font><b> such that </b><br/><a NAME="E5:113_2_2_1"/><i><font color="Green">E486</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font>,<font color="Maroon">w</font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/><b>set </b><font color="Maroon">adl</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font>;<br/><div><i><font color="Green">E487</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1_1"/><i><font color="Green">E488</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><a NAME="E2:113_2_2_1_1"/>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><b>hence </b><a NAME="E3:113_2_2_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_1_2"/><i><font color="Green">E489</font></i>: 
not the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font>
 ;<br/><a NAME="E2:113_2_2_1_2"/><i><font color="Green">E490</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">adl</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font> <a href="fsm_1.html#K3" target="_self">leads_to_under</a> <font color="Maroon">w</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <b>by </b><i>, , </i>;<br/><a NAME="E5:113_2_2_1_2"/><i><font color="Green">E491</font></i>: 
 <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font> is <a href="fsm_1.html#V4" target="_self">final</a>
 <b>by </b><i/>;<br/><a NAME="E6:113_2_2_1_2"/>
for <font color="Olive">Y</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>  holds <br/>(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> or  not <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:113_2_2_1_2_1"/>
 ex <font color="Olive">Y</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span> st <br/>( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> &amp; <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">Y</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span><b> such that </b><br/><a NAME="E3:113_2_2_1_2_1"/><i><font color="Green">E492</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">adl</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> <b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:113_2_2_1_2_1"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" target="_self">the_reduction_of</a> <font color="Maroon">tfsm</font></span>)</span>
 
;<br/>
<a NAME="E6:113_2_2_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="fsm_1.html#K8" target="_self">final_states_partition</a> <font color="Maroon">tfsm</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:113_2_2_1_2_1"/><b>then </b>
<font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E8:113_2_2_1_2_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E7:113_2_2_1_2"/><b>then </b>
not <font color="Maroon">q</font>,<font color="Maroon">adl</font> <a href="fsm_1.html#R5" target="_self">-are_equivalent</a> 
 <b>by </b><i>, , </i>;<br/><b>then consider </b><font color="Maroon">dseq</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">IAlph</font><b> such that </b><br/><a NAME="E9:113_2_2_1_2"/><i><font color="Green">E493</font></i>: 
<font color="Maroon">q</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">adl</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">adl2</font> = <font color="Maroon">adl</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> ;<br/><b>reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> ;<br/><a NAME="E12:113_2_2_1_2"/><i><font color="Green">E494</font></i>: 
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font>,<font color="Maroon">w</font> <a href="fsm_1.html#R1" target="_self">-leads_to</a> <font color="Maroon">adl2</font>
 <b>by </b><i/>;<br/><a NAME="E13:113_2_2_1_2"/>
<font color="Maroon">q</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i>, </i>;<br/><a NAME="E14:113_2_2_1_2"/><b>then </b>
<font color="Maroon">q1</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">adl2</font>,<font color="Maroon">dseq</font> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i>, , </i>;<br/><a NAME="E15:113_2_2_1_2"/><b>then </b>
the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm2</font>,<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">dseq</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">CRtfsm1</font>,<span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">dseq</font></span>)</span> <a href="fsm_1.html#K4" target="_self">-response</a> 
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E16:113_2_2_1_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:113_2_2_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2"/><i><font color="Green">E495</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2"/><i><font color="Green">E496</font></i>: 
<font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">Q</font> = <font color="Maroon">Q</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">Q'</font> = <font color="Maroon">Q</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">q</font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font><b> such that </b><br/><a NAME="E6:113_2_2_2"/><i><font color="Green">E497</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_2_2"/><i><font color="Green">E498</font></i>: 
<font color="Maroon">Q'</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_2_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1"/><i><font color="Green">E499</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">Q''</font> = <font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>;<br/><div><i><font color="Green">E500</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2_1_1_1"/><i><font color="Green">E501</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2_1_1_1"/><i><font color="Green">E502</font></i>: 
for <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font>  holds <br/>( <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> or <font color="Olive">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">z</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font><b> such that </b><a NAME="E1:113_2_2_2_1_1_1_1"/><i><font color="Green">E503</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> )
 ;<br/>

<a NAME="E2:113_2_2_2_1_1_1_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E3:113_2_2_2_1_1_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_1"/>
(  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  ex <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> st <br/>( <font color="Olive">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> &amp; <font color="Olive">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2_2_2_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:113_2_2_2_1_1_2"/><i><font color="Green">E504</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:113_2_2_2_1_1_2"/><i><font color="Green">E505</font></i>: 
<font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q'</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">Q'</font> = <font color="Maroon">Q'</font> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>reconsider </b><font color="Maroon">Q''</font> = <font color="Maroon">Q'</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font> ;<br/><b>consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm</font><b> such that </b><br/><a NAME="E6:113_2_2_2_1_1_2"/><i><font color="Green">E506</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q''</font>
 <b>by </b><i>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/><a NAME="E7:113_2_2_2_1_1_2"/><i><font color="Green">E507</font></i>: 
<font color="Maroon">Q''</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:113_2_2_2_1_1_2_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1_2_1_1"/><i><font color="Green">E508</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E3:113_2_2_2_1_1_2_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_2_1_1"/>
(  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_2_1_1"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_1_2_1_2"/><i><font color="Green">E509</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 ;<br/><div class="add"><a NAME="E2:113_2_2_2_1_1_2_1_2"/><i><font color="Green">E510</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q'</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i><a class="ref" href="fsm_1.html#D2" target="_self">Def2</a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/><a NAME="E5:113_2_2_2_1_1_2_1_2"/>
(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E6:113_2_2_2_1_1_2_1_2"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="fsm_1.html#D2" target="_self">Def2</a>, <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_2_2_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="113_2_2_2_1_2"><b>suppose </b></a><a NAME="E1:113_2_2_2_1_2"/><i><font color="Green">E511</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Q</font> <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:113_2_2_2_1_2"/>
(  not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">CRtfsm2</font> or <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:113_2_2_2_1_2"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:113_2_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
