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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <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">  for <font color="Olive" title="b1">E</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> <br/>  for <font color="Olive" title="b3">SA</font> being   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 <span class="p1">(<span class="default"><a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Olive" title="b1">E</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Olive" title="b1">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> holds  <font color="Olive" title="b2">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Olive" title="b1">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Olive" title="b3">SA</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b3">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <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">  for <font color="Olive" title="b1">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> <br/>  for <font color="Olive" title="b2">SA</font> being   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 <span class="p1">(<span class="default"><a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> holds  <font color="Olive" title="b1">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Olive" title="b2">SA</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b2">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> ; <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">  for <font color="Olive" title="b1">SA</font> being   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 <span class="p1">(<span class="default"><a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> holds  <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="fsm_3.html#K2" title="FSM_3:func.2">_bool</a> <font color="Olive" title="b1">SA</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">SA</font> be   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 <span class="p1">(<span class="default"><a href="flang_1.html#K9" title="FLANG_1:func.9">Lex</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></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"> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">TS</font> =  <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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #);<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Es</font> = <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>);<br/>
<a NAME="E1:54"/>
 <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 <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>, 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> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D3" target="_self" onmouseover="rs('fsm_3/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<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="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T105" onmouseover="rs('rewrite3/T105')" onmouseout="rh()">REWRITE3:105</a></span>
<br/>.= 
<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #))</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T105" onmouseover="rs('rewrite3/T105')" onmouseout="rh()">REWRITE3:105</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">w</font></span>)</span> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #))</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#T31" target="_self" onmouseover="rs('fsm_3/T31')" onmouseout="rh()">Th31</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<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="c4">SA</font>, the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <font color="Maroon" title="c4">SA</font> #))</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>

<br/>.= 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c4">SA</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T105" onmouseover="rs('rewrite3/T105')" onmouseout="rh()">REWRITE3:105</a></span>
;<br/> <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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