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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fsm_1.html#L1">FSM</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:9"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="fsm_2.html#V1" target="_self">calculating_type</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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="E2:9"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E3:9"/><i><font color="Green">E8</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>3</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>4</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="fsm_1.html#D2">FSM_1:def 2</a></i>;<br/>
<a NAME="E4:9"/>
 <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>3</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font>, <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>4</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="txt" href="fsm_2.html#E1:9"><i><font color="Green">E6</font></i></a>, <a class="txt" href="fsm_2.html#E2:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="fsm_2.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
 <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>3</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="fsm_2.html#NK1" target="_self">GEN</a> <font color="Maroon">c<sub>4</sub></font>,the <a href="fsm_1.html#U2">InitS</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="fsm_2.html#E2:9"><i><font color="Green">E7</font></i></a>, <a class="txt" href="fsm_2.html#E3:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="trees_1.html#T19">TREES_1:19</a></i>;<br/>


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