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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">CRtfsm1</font>, <font color="Olive" title="b3">CRtfsm2</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#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>  st <font color="Olive" title="b1">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="b3">CRtfsm2</font> holds <br/>for <font color="Olive" title="b4">Q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Olive" title="b1">tfsm</font></span>)</span><br/> for <font color="Olive" title="b5">q1</font>, <font color="Olive" title="b6">q2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b4">Q</font>  holds <br/>(  not <font color="Olive" title="b5">q1</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="Olive" title="b3">CRtfsm2</font> or  not <font color="Olive" title="b6">q2</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="Olive" title="b3">CRtfsm2</font> or  not <font color="Olive" title="b5">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q2</font> )</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">CRtfsm1</font>, <font color="Olive" title="b2">CRtfsm2</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#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>  st <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Olive" title="b2">CRtfsm2</font> holds <br/>for <font color="Olive" title="b3">Q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font></span>)</span><br/> for <font color="Olive" title="b4">q1</font>, <font color="Olive" title="b5">q2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">Q</font>  holds <br/>(  not <font color="Olive" title="b4">q1</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="Olive" title="b2">CRtfsm2</font> or  not <font color="Olive" title="b5">q2</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="Olive" title="b2">CRtfsm2</font> or  not <font color="Olive" title="b4">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">q2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">CRtfsm1</font>, <font color="Maroon" title="c5">CRtfsm2</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#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"> ( <font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c5">CRtfsm2</font> implies for <font color="Olive" title="b1">Q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font></span>)</span><br/> for <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Q</font>  holds <br/>(  not <font color="Olive" title="b2">q1</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="c5">CRtfsm2</font> or  not <font color="Olive" title="b3">q2</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="c5">CRtfsm2</font> or  not <font color="Olive" title="b2">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q2</font> ) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">rtfsm1</font> = <font color="Maroon" title="c4">CRtfsm1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">rtfsm2</font> = <font color="Maroon" title="c5">CRtfsm2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">rtfsm</font> =  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">tfsm2</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><span class="kw"> such that </span><br/><a NAME="E2:116"/><span class="lab"><font color="Green" title="E80">A1</font></span>: 
<font color="Maroon" title="c5">CRtfsm2</font>, <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font> <a href="fsm_1.html#R7" title="FSM_1:pred.7">-are_isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#T65" target="_self" title="FSM_1:th.65">Th65</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">tfsm2r</font> =  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">Tf</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">CRtfsm2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:116"/><span class="lab"><font color="Green" title="E81">A2</font></span>: 
<font color="Maroon" title="c11">Tf</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">and </span><br/><a NAME="E5:116"/>
<font color="Maroon" title="c11">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c5">CRtfsm2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:116"/><span class="lab"><font color="Green" title="E82">A3</font></span>: 
for <font color="Olive" title="b1">q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c5">CRtfsm2</font><br/> for <font color="Olive" title="b2">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font> holds <br/> ( <font color="Maroon" title="c11">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <font color="Maroon" title="c5">CRtfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U1" title="FSM_1:sel.1">Tran</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> &amp; the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c5">CRtfsm2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">q</font>,<font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Tf</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font></span>)</span>,<font color="Olive" title="b2">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:116"><span class="lab"><font color="Green" title="E80">A1</font></span></a>, <a class="ref" href="fsm_1.html#D19" target="_self" title="FSM_1:def.19">Def19</a></span>;<br/>
<span class="kw">assume </span><a NAME="E7:116"/><span class="lab"><font color="Green" title="E83">A4</font></span>: 
<font color="Maroon" title="c3">tfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">CRtfsm1</font> <a href="fsm_1.html#K13" title="FSM_1:func.13">-Mealy_union</a> <font color="Maroon" title="c5">CRtfsm2</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">Q</font> being  <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font></span>)</span><br/> for <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Q</font>  holds <br/>(  not <font color="Olive" title="b2">q1</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="c5">CRtfsm2</font> or  not <font color="Olive" title="b3">q2</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="c5">CRtfsm2</font> or  not <font color="Olive" title="b2">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q2</font> )</span><br/>

<a NAME="E8:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A5</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">tfsm</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="c4">CRtfsm1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">CRtfsm2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D24" target="_self" title="FSM_1:def.24">Def24</a></span>;<br/>
<span class="kw">given </span><font color="Maroon" title="c12">Q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font></span>)</span>, <font color="Maroon" title="c13">q1</font>, <font color="Maroon" title="c14">q2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c12">Q</font><span class="kw"> such that </span><a NAME="E10:116"/><span class="lab"><font color="Green" title="E85">A6</font></span>: 
<font color="Maroon" title="c13">q1</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="c5">CRtfsm2</font>
 <span class="kw">and </span><br/><a NAME="E11:116"/><span class="lab"><font color="Green" title="E86">A7</font></span>: 
<font color="Maroon" title="c14">q2</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="c5">CRtfsm2</font>
 <span class="kw">and </span><br/><a NAME="E12:116"/><span class="lab"><font color="Green" title="E87">A8</font></span>: 
<font color="Maroon" title="c13">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E13:116"/><span class="lab"><font color="Green" title="E88">A9</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c11">Tf</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="c5">CRtfsm2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E14:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A10</font></span>: 
<font color="Maroon" title="c11">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">q1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">q2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:116"><span class="lab"><font color="Green" title="E85">A6</font></span></a>, <a class="txt" href="#E11:116"><span class="lab"><font color="Green" title="E86">A7</font></span></a>, <a class="txt" href="#E12:116"><span class="lab"><font color="Green" title="E87">A8</font></span></a>, <a class="txt" href="#E4:116"><span class="lab"><font color="Green" title="E81">A2</font></span></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></span>;<br/>
<a NAME="E15:116"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c11">Tf</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 <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:116"><span class="lab"><font color="Green" title="E81">A2</font></span></a>, <a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">Tq1</font> = <font color="Maroon" title="c11">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">q1</font>, <font color="Maroon" title="c16">Tq2</font> = <font color="Maroon" title="c11">Tf</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">q2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c9">tfsm2</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:116"><span class="lab"><font color="Green" title="E85">A6</font></span></a>, <a class="txt" href="#E11:116"><span class="lab"><font color="Green" title="E86">A7</font></span></a>, <a class="txt" href="#E13:116"><span class="lab"><font color="Green" title="E88">A9</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">q2</font> = <font color="Maroon" title="c14">q2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">tfsm</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:116"><span class="lab"><font color="Green" title="E86">A7</font></span></a>, <a class="txt" href="#E8:116"><span class="lab"><font color="Green" title="E84">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">q29</font> = <font color="Maroon" title="c17">q2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">CRtfsm2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:116"><span class="lab"><font color="Green" title="E86">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">q1</font> = <font color="Maroon" title="c13">q1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">tfsm</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:116"><span class="lab"><font color="Green" title="E85">A6</font></span></a>, <a class="txt" href="#E8:116"><span class="lab"><font color="Green" title="E84">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">q19</font> = <font color="Maroon" title="c19">q1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">CRtfsm2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:116"><span class="lab"><font color="Green" title="E85">A6</font></span></a></span>;<br/>
<a NAME="E21:116"/>
not <font color="Maroon" title="c15">Tq1</font>,<font color="Maroon" title="c16">Tq2</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="txt" href="#E14:116"><span class="lab"><font color="Green" title="E89">A10</font></span></a>, <a class="ref" href="fsm_1.html#T62" target="_self" title="FSM_1:th.62">Th62</a></span>;<br/>
<a NAME="E22:116"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A11</font></span>: 
not <font color="Maroon" title="c20">q19</font>,<font color="Maroon" title="c18">q29</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="txt" href="#E6:116"><span class="lab"><font color="Green" title="E82">A3</font></span></a>, <a class="ref" href="fsm_1.html#T61" target="_self" title="FSM_1:th.61">Th61</a></span>;<br/>
<a NAME="E23:116"/><span class="lab"><font color="Green" title="E91">A12</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c3">tfsm</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_1.html#K8" title="FSM_1:func.8">final_states_partition</a> <font color="Maroon" title="c3">tfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D18" target="_self" title="FSM_1:def.18">Def18</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">Q</font> = <font color="Maroon" title="c12">Q</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">tfsm</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E25:116"/><span class="lab"><font color="Green" title="E92">A13</font></span>: 
 <a href="fsm_1.html#K8" title="FSM_1:func.8">final_states_partition</a> <font color="Maroon" title="c3">tfsm</font> is  <a href="fsm_1.html#V4" title="FSM_1:attr.4">final</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D15" target="_self" title="FSM_1:def.15">Def15</a></span>;<br/>
<a NAME="E26:116"/>
<font color="Maroon" title="c21">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:116"><span class="lab"><font color="Green" title="E91">A12</font></span></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></span>;<br/>
<a NAME="E27:116"/><span class="kw">then </span>
<font color="Maroon" title="c19">q1</font>,<font color="Maroon" title="c17">q2</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="txt" href="#E25:116"><span class="lab"><font color="Green" title="E92">A13</font></span></a>, <a class="txt" href="#E23:116"><span class="lab"><font color="Green" title="E91">A12</font></span></a>, <a class="ref" href="fsm_1.html#D14" target="_self" title="FSM_1:def.14">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E28:116"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:116"><span class="lab"><font color="Green" title="E83">A4</font></span></a>, <a class="txt" href="#E22:116"><span class="lab"><font color="Green" title="E90">A11</font></span></a>, <a class="ref" href="fsm_1.html#T77" target="_self" title="FSM_1:th.77">Th77</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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