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<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E1:33_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>2</sub></font> holds <br/> <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Olive">b<sub>1</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Olive">b<sub>2</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:33_1_1_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> =  <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>7</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>, <font color="Maroon">c<sub>10</sub></font> =  <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>8</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> as   <a href="finseq_1.html#NM1">FinSequence</a> ;<br/>
<i><font color="Green">E18</font></i>: <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> 1 = 
the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="fsm_1.html#D2">FSM_1:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="fsm_1.html#D2">FSM_1:def 2</a></i>
;<br/>
<a NAME="E4:33_1_1_1"/><i><font color="Green">E19</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="fsm_2.html#E1:33_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="fsm_1.html#D2">FSM_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:33_1_1_1_2"/><i><font color="Green">E20</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:33_1_1_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><a NAME="E3:33_1_1_1_2"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 <b>by </b><i><a class="txt" href="fsm_2.html#E1:33_1_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E4:33_1_1_1_2"/><b>then </b>
not <!--HUMANRECFAILED-->( not <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="txt" href="fsm_2.html#E1:33_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="fsm_2.html#E3:33_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="fsm_2.html#E4:33_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fsm_2.html#E2:33_1_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="fsm_2.html#T17" target="_self">Th17</a></i>;<br/><b>hence </b><a NAME="E5:33_1_1_1_2"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> implies <font color="Maroon">c<sub>9</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:33_1_1_1"/>
 <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>7</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>8</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="fsm_2.html#E4:33_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:33_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="fsm_2.html#K1" target="_self">-TwoStatesMooreSM</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> is <a href="fsm_2.html#V1" target="_self">calculating_type</a>
 <b>by </b><i><a class="ref" href="fsm_2.html#T7" target="_self">Th7</a></i>;<br/>


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