<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">Stfsm1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font>;<br/>
<b>set </b><font color="Maroon">Stfsm2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>;<br/>
<b>set </b><font color="Maroon">Trtfsm1</font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font>;<br/>
<b>set </b><font color="Maroon">Trtfsm2</font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font>;<br/>
<b>set </b><font color="Maroon">Oftfsm1</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font>;<br/>
<b>set </b><font color="Maroon">Oftfsm2</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font>;<br/>
<b>set </b><font color="Maroon">Tr</font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font>;<br/>
<b>set </b><font color="Maroon">Of</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font>;<br/>
<b>reconsider </b><font color="Maroon">S</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E2:102_1_1"/><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:102_1_1"/>
 <a href="relat_1.html#K1">dom</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E23</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font></span>)</span> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font></span>)</span>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T120">ZFMISC_1:120</a></i>
;<br/>
<a NAME="E5:102_1_1"/><i><font color="Green">E38</font></i>: 
(  <a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> &amp;  <a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font> )
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:102_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/>
<a NAME="E7:102_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E8:102_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">Tr</font> = the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">S</font> <b>by </b><i>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E10:102_1_1"/><i><font color="Green">E40</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:102_1_1"/>
 <a href="relat_1.html#K1">dom</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E42</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font></span>)</span> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font></span>)</span>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T120">ZFMISC_1:120</a></i>
;<br/>
<a NAME="E13:102_1_1"/><i><font color="Green">E43</font></i>: 
(  <a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">OAlph</font> &amp;  <a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">OAlph</font> )
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E14:102_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a></i>;<br/>
<a NAME="E15:102_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">OAlph</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">OAlph</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E16:102_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">OAlph</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">OAlph</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">Of</font> = the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">IAlph</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">OAlph</font> <b>by </b><i><a class="ref" href="fsm_1.html#T15" target="_self">Th15</a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">IS</font> = the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">tfsm1</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>take </b>
 <a href="fsm_1.html#G2" target="_self">Mealy-FSM</a>(# <font color="Maroon">S</font>,<font color="Maroon">Tr</font>,<font color="Maroon">Of</font>,<font color="Maroon">IS</font> #)
;<br/>

<b>thus </b><a NAME="E19:102_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <a href="fsm_1.html#G2" target="_self">Mealy-FSM</a>(# <font color="Maroon">S</font>,<font color="Maroon">Tr</font>,<font color="Maroon">Of</font>,<font color="Maroon">IS</font> #) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">tfsm2</font> &amp; the <a href="fsm_1.html#U1" target="_self">Tran</a> of <a href="fsm_1.html#G2" target="_self">Mealy-FSM</a>(# <font color="Maroon">S</font>,<font color="Maroon">Tr</font>,<font color="Maroon">Of</font>,<font color="Maroon">IS</font> #) <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U1" target="_self">Tran</a> of <font color="Maroon">tfsm2</font> &amp; the <a href="fsm_1.html#U3" target="_self">OFun</a> of <a href="fsm_1.html#G2" target="_self">Mealy-FSM</a>(# <font color="Maroon">S</font>,<font color="Maroon">Tr</font>,<font color="Maroon">Of</font>,<font color="Maroon">IS</font> #) <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm1</font> <a href="funct_4.html#K1">+*</a> the <a href="fsm_1.html#U3" target="_self">OFun</a> of <font color="Maroon">tfsm2</font> &amp; the <a href="fsm_1.html#U2" target="_self">InitS</a> of <a href="fsm_1.html#G2" target="_self">Mealy-FSM</a>(# <font color="Maroon">S</font>,<font color="Maroon">Tr</font>,<font color="Maroon">Of</font>,<font color="Maroon">IS</font> #) <a href="hidden.html#R1">=</a> the <a href="fsm_1.html#U2" target="_self">InitS</a> of <font color="Maroon">tfsm1</font> )
 ;<br/>


</div>
