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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">rtfsm</font>, <font color="Olive" title="b2">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="b3">qr1</font>, <font color="Olive" title="b4">qr2</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">rtfsm</font>  st <font color="Olive" title="b1">rtfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Olive" title="b2">tfsm</font> &amp; <font color="Olive" title="b3">qr1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">qr2</font> holds <br/> not <font color="Olive" title="b3">qr1</font>,<font color="Olive" title="b4">qr2</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">rtfsm</font>, <font color="Maroon" title="c4">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">qr1</font>, <font color="Olive" title="b2">qr2</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">rtfsm</font>  st <font color="Maroon" title="c3">rtfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">tfsm</font> &amp; <font color="Olive" title="b1">qr1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">qr2</font> holds <br/> not <font color="Olive" title="b1">qr1</font>,<font color="Olive" title="b2">qr2</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="c5">qr1</font>, <font color="Maroon" title="c6">qr2</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c3">rtfsm</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">rtfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">tfsm</font> &amp; <font color="Maroon" title="c5">qr1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">qr2</font> implies  not <font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c6">qr2</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:72"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c3">rtfsm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_1.html#K11" title="FSM_1:func.11">the_reduction_of</a> <font color="Maroon" title="c4">tfsm</font>
 <span class="kw">and </span><br/><a NAME="E2:72"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c5">qr1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">qr2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c6">qr2</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> </span><br/>

<a NAME="E3:72"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">rtfsm</font> <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="c4">tfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <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="c7">q19</font> = <font color="Maroon" title="c5">qr1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">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/>
<span class="kw">consider </span><font color="Maroon" title="c8">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">tfsm</font><span class="kw"> such that </span><br/><a NAME="E6:72"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">q19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="finseq_4.html#T87" title="FINSEQ_4:th.87">FINSEQ_4:87</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">q29</font> = <font color="Maroon" title="c6">qr2</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">tfsm</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">tfsm</font><span class="kw"> such that </span><br/><a NAME="E9:72"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">q29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="finseq_4.html#T87" title="FINSEQ_4:th.87">FINSEQ_4:87</a></span>;<br/>
<a NAME="E10:72"/><span class="lab"><font color="Green" title="E58">A6</font></span>: 
 <a href="fsm_1.html#K8" title="FSM_1:func.8">final_states_partition</a> <font color="Maroon" title="c4">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="E11:72"/>
 not <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c10">y</font> <a href="fsm_1.html#R5" title="FSM_1:pred.5">-are_equivalent</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:72_1"/>
<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c10">y</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="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">X</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">rtfsm</font><span class="kw"> such that </span><br/><a NAME="E3:72_1"/><span class="lab"><font color="Green" title="E59">A7</font></span>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X</font> &amp; <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E10:72"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="ref" href="fsm_1.html#D14" target="_self" title="FSM_1:def.14">Def14</a></span>;<br/>
<a NAME="E4:72_1"/><span class="lab"><font color="Green" title="E60">A8</font></span>: 
<font color="Maroon" title="c9">q29</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">q19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="eqrel_1.html#D4" title="EQREL_1:def.4">EQREL_1:def 4</a></span>;<br/>
<a NAME="E5:72_1"/>
<font color="Maroon" title="c11">X</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">tfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E6:72_1"/><span class="kw">then </span>
( <font color="Maroon" title="c11">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">q19</font> or <font color="Maroon" title="c11">X</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">q19</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="eqrel_1.html#D4" title="EQREL_1:def.4">EQREL_1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:72_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:72"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="txt" href="#E9:72"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="txt" href="#E3:72_1"><span class="lab"><font color="Green" title="E59">A7</font></span></a>, <a class="txt" href="#E4:72_1"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">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="E13:72"/><span class="lab"><font color="Green" title="E59">A9</font></span>: 
(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">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="c10">y</font>,<font color="Maroon" title="c11">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/>
<span class="kw">set </span><font color="Maroon" title="c12">q1adm</font> = (<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">q2adm</font> = (<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">xadm</font> = (<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">yadm</font> = (<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">xresp</font> = (<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">yresp</font> = (<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c18">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E16:72"/><span class="lab"><font color="Green" title="E60">A10</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c18">k</font> &amp; <font color="Maroon" title="c18">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E17:72"/><span class="lab"><font color="Green" title="E61">A11</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:72"><span class="lab"><font color="Green" title="E59">A9</font></span></a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>;<br/>
<a NAME="E18:72"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>;<br/>
<a NAME="E19:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A12</font></span>: 
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:72"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E20:72"/><span class="kw">then </span>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T8" title="FINSEQ_2:th.8">FINSEQ_2:8</a></span>;<br/>
<a NAME="E21:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A13</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E9:72"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="fsm_1.html#T40" target="_self" title="FSM_1:th.40">Th57</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">q1resp</font> = (<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">q2resp</font> = (<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="lab"><font color="Green" title="E64">A14</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
;<br/>
<a NAME="E23:72"/>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:72"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E24:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A15</font></span>: 
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:72"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="ref" href="finseq_2.html#T8" title="FINSEQ_2:th.8">FINSEQ_2:8</a></span>;<br/>
<a NAME="E25:72"/><span class="kw">then </span>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E26:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A16</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">rtfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
;<br/>
<a NAME="E28:72"/><span class="kw">then </span>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:72"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E29:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A17</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">rtfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
<a NAME="E30:72"/>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c11">w</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:72"><span class="lab"><font color="Green" title="E62">A12</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E31:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A18</font></span>: 
<font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IAlph</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
<span class="lab"><font color="Green" title="E69">A19</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
;<br/>
<a NAME="E33:72"/><span class="kw">then </span>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:72"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E34:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A20</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">tfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D2" target="_self" title="FSM_1:def.2">Def2</a></span>
;<br/>
<a NAME="E36:72"/><span class="kw">then </span>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:72"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="txt" href="#E32:72"><span class="lab"><font color="Green" title="E69">A19</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E37:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A21</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">tfsm</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
<a NAME="E38:72"/>
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:72"><span class="lab"><font color="Green" title="E62">A12</font></span></a>, <a class="ref" href="finseq_2.html#T8" title="FINSEQ_2:th.8">FINSEQ_2:8</a></span>;<br/>
<a NAME="E39:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A22</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E6:72"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="fsm_1.html#T40" target="_self" title="FSM_1:th.40">Th57</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_7"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:72_7"/><span class="lab"><font color="Green" title="E73">A23</font></span>: 
(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">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="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:72_7"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>;<br/><a NAME="E3:72_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A24</font></span>: 
<font color="Maroon" title="c18">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c11">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:72"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><a NAME="E4:72_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A25</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</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 <font color="Maroon" title="c4">tfsm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>;<br/><span class="lab"><font color="Green" title="E76">A26</font></span>: <span class="p1">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> = 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">rtfsm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c6">qr2</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_7"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E31:72"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="txt" href="#E29:72"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="txt" href="#E21:72"><span class="lab"><font color="Green" title="E63">A13</font></span></a>, <a class="txt" href="#E37:72"><span class="lab"><font color="Green" title="E71">A21</font></span></a>, <a class="ref" href="fsm_1.html#D18" target="_self" title="FSM_1:def.18">Def18</a></span>
;<br/><span class="p1">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font> = 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c3">rtfsm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_7"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>
<br/>.= 
 the <a href="fsm_1.html#U3" title="FSM_1:sel.3">OFun</a> of <font color="Maroon" title="c4">tfsm</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c11">w</font>) <a href="fsm_1.html#K2" title="FSM_1:func.2">-admissible</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">k</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E26:72"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="txt" href="#E31:72"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="txt" href="#E39:72"><span class="lab"><font color="Green" title="E72">A22</font></span></a>, <a class="txt" href="#E34:72"><span class="lab"><font color="Green" title="E70">A20</font></span></a>, <a class="ref" href="fsm_1.html#D18" target="_self" title="FSM_1:def.18">Def18</a></span>
;<br/><span class="kw">hence </span><a NAME="E7:72_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:72"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="txt" href="#E1:72_7"><span class="lab"><font color="Green" title="E73">A23</font></span></a>, <a class="txt" href="#E3:72_7"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E5:72_7"><span class="lab"><font color="Green" title="E76">A26</font></span></a>, <a class="txt" href="#E4:72_7"><span class="lab"><font color="Green" title="E75">A25</font></span></a>, <a class="ref" href="fsm_1.html#D6" target="_self" title="FSM_1:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E41:72"/>
 not <font color="Maroon" title="c5">qr1</font>,<font color="Maroon" title="c6">qr2</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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
