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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">w1</font>, <font color="Olive" title="b2">w2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</font><br/>  for <font color="Olive" title="b3">tfsm1</font>, <font color="Olive" title="b4">tfsm2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font><br/>  for <font color="Olive" title="b5">q11</font>, <font color="Olive" title="b6">q12</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b3">tfsm1</font><br/>  for <font color="Olive" title="b7">q21</font>, <font color="Olive" title="b8">q22</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b4">tfsm2</font>  st <font color="Olive" title="b5">q11</font>,<font color="Olive" title="b1">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b6">q12</font> &amp; <font color="Olive" title="b7">q21</font>,<font color="Olive" title="b1">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b8">q22</font> &amp; (<font color="Olive" title="b6">q12</font>,<font color="Olive" title="b2">w2</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="Olive" title="b8">q22</font>,<font color="Olive" title="b2">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  holds <br/>(<font color="Olive" title="b5">q11</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">w2</font></span>)</span>) <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="Olive" title="b7">q21</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">w1</font>, <font color="Maroon" title="c4">w2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">IAlph</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">tfsm1</font>, <font color="Olive" title="b2">tfsm2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font><br/>  for <font color="Olive" title="b3">q11</font>, <font color="Olive" title="b4">q12</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b1">tfsm1</font><br/>  for <font color="Olive" title="b5">q21</font>, <font color="Olive" title="b6">q22</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Olive" title="b2">tfsm2</font>  st <font color="Olive" title="b3">q11</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b4">q12</font> &amp; <font color="Olive" title="b5">q21</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b6">q22</font> &amp; (<font color="Olive" title="b4">q12</font>,<font color="Maroon" title="c4">w2</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="Olive" title="b6">q22</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  holds <br/>(<font color="Olive" title="b3">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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="Olive" title="b5">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">tfsm1</font>, <font color="Maroon" title="c6">tfsm2</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L2" title="FSM_1:struct.2">Mealy-FSM</a> of <font color="Maroon" title="c1">IAlph</font>,<font color="Maroon" title="c2">OAlph</font>; <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">q11</font>, <font color="Olive" title="b2">q12</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c5">tfsm1</font><br/>  for <font color="Olive" title="b3">q21</font>, <font color="Olive" title="b4">q22</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c6">tfsm2</font>  st <font color="Olive" title="b1">q11</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b2">q12</font> &amp; <font color="Olive" title="b3">q21</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b4">q22</font> &amp; (<font color="Olive" title="b2">q12</font>,<font color="Maroon" title="c4">w2</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="Olive" title="b4">q22</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  holds <br/>(<font color="Olive" title="b1">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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="Olive" title="b3">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">q11</font>, <font color="Maroon" title="c8">q12</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c5">tfsm1</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">q21</font>, <font color="Olive" title="b2">q22</font> being   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c6">tfsm2</font>  st <font color="Maroon" title="c7">q11</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c8">q12</font> &amp; <font color="Olive" title="b1">q21</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Olive" title="b2">q22</font> &amp; (<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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="Olive" title="b2">q22</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  holds <br/>(<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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="Olive" title="b1">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c9">q21</font>, <font color="Maroon" title="c10">q22</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c6">tfsm2</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="c7">q11</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c8">q12</font> &amp; <font color="Maroon" title="c9">q21</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c10">q22</font> &amp; (<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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">q22</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  implies (<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> (<font color="Maroon" title="c9">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:27"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c7">q11</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c8">q12</font>
 <span class="kw">and </span><br/><a NAME="E2:27"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c9">q21</font>,<font color="Maroon" title="c3">w1</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> <font color="Maroon" title="c10">q22</font>
 <span class="kw">and </span><br/><a NAME="E3:27"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
(<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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">q22</font>,<font color="Maroon" title="c4">w2</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"> (<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> (<font color="Maroon" title="c9">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c11">r12</font> = (<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">r22</font> = (<font color="Maroon" title="c10">q22</font>,<font color="Maroon" title="c4">w2</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<a NAME="E4:27"/><span class="lab"><font color="Green" title="E21">A4</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="c10">q22</font>,<font color="Maroon" title="c4">w2</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="c4">w2</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/>
<span class="kw">set </span><font color="Maroon" title="c13">w</font> = <font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">r1w1</font> = (<font color="Maroon" title="c7">q11</font>,<font color="Maroon" title="c3">w1</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">r2w1</font> = (<font color="Maroon" title="c9">q21</font>,<font color="Maroon" title="c3">w1</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<span class="kw">assume </span><a NAME="E5:27"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
(<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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="c9">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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/>

<span class="kw">set </span><font color="Maroon" title="c16">r21</font> = (<font color="Maroon" title="c9">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<a NAME="E6:27"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
(<font color="Maroon" title="c9">q21</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c9">q21</font>,<font color="Maroon" title="c3">w1</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">q22</font>,<font color="Maroon" title="c4">w2</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="txt" href="#E2:27"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="fsm_1.html#T11" target="_self" title="FSM_1:th.11">Th26</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">r11</font> = (<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a> ;<br/>
<a NAME="E7:27"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
(<font color="Maroon" title="c7">q11</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c7">q11</font>,<font color="Maroon" title="c3">w1</font>) <a href="fsm_1.html#K4" title="FSM_1:func.4">-response</a></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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="txt" href="#E1:27"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="fsm_1.html#T11" target="_self" title="FSM_1:th.11">Th26</a></span>;<br/>
<a NAME="E8:27"/><span class="lab"><font color="Green" title="E25">A8</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="c7">q11</font>,<font color="Maroon" title="c3">w1</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="c3">w1</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="E9:27"/><span class="lab"><font color="Green" title="E26">A9</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="c8">q12</font>,<font color="Maroon" title="c4">w2</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="c4">w2</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="E10:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">q12</font>,<font color="Maroon" title="c4">w2</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="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E11:27"/><span class="kw">then </span>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">q12</font>,<font color="Maroon" title="c4">w2</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="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c18">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E13:27"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<font color="Maroon" title="c18">j</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="c4">w2</font>
 <span class="kw">and </span><br/><a NAME="E14:27"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c10">q22</font>,<font color="Maroon" title="c4">w2</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">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="finseq_2.html#T9" title="FINSEQ_2:th.9">FINSEQ_2:9</a></span>;<br/>
<a NAME="E15:27"/><span class="lab"><font color="Green" title="E30">A13</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="c9">q21</font>,<font color="Maroon" title="c3">w1</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="c3">w1</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="E16:27"/>
<font color="Maroon" title="c18">j</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">q12</font>,<font color="Maroon" title="c4">w2</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="txt" href="#E10:27"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E28">A11</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="E17:27"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<span class="p1">(<span class="default">(<font color="Maroon" title="c7">q11</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">w1</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c4">w2</font></span>)</span>) <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> <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="c3">w1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c18">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c8">q12</font>,<font color="Maroon" title="c4">w2</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">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E7:27"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/>
<a NAME="E18:27"/>
<font color="Maroon" title="c18">j</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">q22</font>,<font color="Maroon" title="c4">w2</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="txt" href="#E9:27"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E10:27"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E13:27"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:27"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E15:27"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E14:27"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E6:27"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E17:27"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</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>
