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<span class="kw">reconsider </span><font color="Maroon" title="c4">SA</font> =  <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="c3">A</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c3">A</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c3">A</font> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_3.html#L1" title="FSM_3:struct.1">semiautomaton</a> over <font color="Maroon" title="c2">F</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">cA</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">tA</font> =  the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> 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"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>,<span class="p2">(<span class="default"><a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Maroon" title="c1">E</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">iA</font> =  the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>;<br/>
<a NAME="E3:32_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> : <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font> </span> } </span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] <span class="kw">means </span>$1 <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font>;<br/>
<a NAME="E1:32_1_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">Q</font>] </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="fraenkel.html#S10" onmouseover="rs('fraenkel/S10')" onmouseout="rh()">FRAENKEL:sch 10</a>();<br/></span>
<span class="kw">hence </span><a NAME="E2:32_1_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> : <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font> </span> } </span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">fA</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> : <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font> </span> } </span>  as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">bA</font> =  <a href="fsm_3.html#G2" title="FSM_3:aggr.2">automaton</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>,<font color="Maroon" title="c6">tA</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>,<font color="Maroon" title="c8">fA</font> #);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">bA</font> =  <a href="fsm_3.html#G2" title="FSM_3:aggr.2">automaton</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>,<font color="Maroon" title="c6">tA</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Maroon" title="c4">SA</font></span>)</span>,<font color="Maroon" title="c8">fA</font> #) as   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_3.html#V3" title="FSM_3:attr.3">strict</a>   <a href="fsm_3.html#V4" title="FSM_3:attr.4">deterministic</a>   <a href="fsm_3.html#L2" title="FSM_3:struct.2">automaton</a> over  <a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Maroon" title="c1">E</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D5" target="_self" onmouseover="rs('fsm_3/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">bA</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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="c10">bA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c10">bA</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c10">bA</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <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="c3">A</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c3">A</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c3">A</font> #) &amp;  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c10">bA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">bA</font> : <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font> </span> } </span>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:32_1_1"/>
(  <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="c10">bA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c10">bA</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c10">bA</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <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="c3">A</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c3">A</font>, the <a href="fsm_3.html#U1" title="FSM_3:sel.1">InitS</a> of <font color="Maroon" title="c3">A</font> #) &amp;  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c10">bA</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">bA</font> : <font color="Olive" title="b1">Q</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <font color="Maroon" title="c3">A</font> </span> } </span>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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