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<span class="kw">consider </span><font color="Maroon" title="c3">X</font> being  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/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">T</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</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">X</font>,<font color="Maroon" title="c2">F</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c3">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T25" title="RELSET_1:th.25">RELSET_1:25</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">I</font> = <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> ;<br/>
<span class="kw">take </span><font color="Maroon" title="c7">A</font> =  <a href="fsm_3.html#G2" title="FSM_3:aggr.2">automaton</a>(# <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">T</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c6">I</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V3" title="FSM_3:attr.3">strict</a>  &amp; not <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  &amp; <font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:31_1_1"/>
<font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V3" title="FSM_3:attr.3">strict</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  &amp; <font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:31_1_1"/>
not <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">A</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  &amp; <font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:31_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">A</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a> </span><br/>

<a NAME="E8:31_1_1"/>
(  <a href="rewrite3.html#G1" title="REWRITE3:aggr.1">transition-system</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">A</font>,the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c7">A</font> #) is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a>, <a class="ref" href="rewrite3.html#T14" title="REWRITE3:th.14">REWRITE3:14</a></span>;<br/>
<a NAME="E9:31_1_1"/><span class="kw">then </span>
 <a href="fsm_3.html#G1" title="FSM_3:aggr.1">semiautomaton</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c7">A</font>,the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c7">A</font>,the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c7">A</font> #) is  <a href="fsm_3.html#V2" title="FSM_3:attr.2">deterministic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D2" target="_self" title="FSM_3:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:31_1_1"/>
<font color="Maroon" title="c7">A</font> is  <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D5" target="_self" title="FSM_3:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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