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<b>reconsider </b><font color="Maroon" title="c3">S</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">IS</font> = 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">S</font> <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">dF</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c6">Tr</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="borsuk_1.html#K1" title="BORSUK_1:func.1">--&gt;</a> 1;<br/>
<a NAME="E3:93_1_1"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="borsuk_1.html#K1" title="BORSUK_1:func.1">--&gt;</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="borsuk_1.html#K1" title="BORSUK_1:func.1">--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">S</font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">T</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="borsuk_1.html#K1" title="BORSUK_1:func.1">--&gt;</a> 1 as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c3">S</font> <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">out</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">OAlph</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">OF</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="borsuk_1.html#K1" title="BORSUK_1:func.1">--&gt;</a> <font color="Maroon" title="c8">out</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c1">IAlph</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c2">OAlph</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">M</font> =  <a href="fsm_1.html#G2" title="FSM_1:aggr.2">Mealy-FSM</a>(# <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c7">T</font>,<font color="Maroon" title="c9">OF</font>,<font color="Maroon" title="c4">IS</font> #) as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">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/>
<b>take </b>
<font color="Maroon" title="c10">M</font>
;<br/>

<b>let </b><font color="Maroon" title="c11">q</font> be   <a href="fsm_1.html#NM1" title="FSM_1:NM.1">State</a> of <font color="Maroon" title="c10">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fsm_1.html#D22" target="_self" title="FSM_1:def.22">FSM_1:def 22</a><br/>

<a NAME="E8:93_1_1"/><i><font color="Green" title="E69">A1</font></i>: 
<font color="Maroon" title="c11">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E9:93_1_1"/>
the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c10">M</font>, <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">IAlph</font> <a href="fsm_1.html#R1" title="FSM_1:pred.1">-leads_to</a> the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Maroon" title="c10">M</font>
 
<b>by </b><i><a class="ref" href="fsm_1.html#T17" target="_self" title="FSM_1:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E10:93_1_1"/>
<font color="Maroon" title="c11">q</font> is <a href="fsm_1.html#V6" title="FSM_1:attr.6">accessible</a>
 <b>by </b><i><a class="txt" href="fsm_1.html#E8:93_1_1"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="fsm_1.html#D21" target="_self" title="FSM_1:def.21">Def21</a></i>;<br/>


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