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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">A</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_3.html#L2" title="FSM_3:struct.2">automaton</a> of <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>  st <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Olive" title="b2">A</font></span>)</span> holds <br/><font color="Maroon" title="c1">X</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="Olive" title="b2">A</font></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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_3.html#L2" title="FSM_3:struct.2">automaton</a> of <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>  st <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Olive" title="b1">A</font></span>)</span> holds <br/><font color="Maroon" title="c1">X</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="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_3.html#L2" title="FSM_3:struct.2">automaton</a> of <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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Maroon" title="c3">A</font></span>)</span> implies <font color="Maroon" title="c1">X</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><br/>





<span class="kw">assume </span><a NAME="E1:57"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Maroon" title="c3">A</font></span>)</span>
 ; <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="c1">X</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><br/>

<a NAME="E2:57"/>
the <a href="fsm_3.html#U2" title="FSM_3:sel.2">FinalS</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Maroon" title="c3">A</font></span>)</span> <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 <span class="p1">(<span class="default"><a href="fsm_3.html#K4" title="FSM_3:func.4">_bool</a> <font color="Maroon" title="c3">A</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D6" target="_self" title="FSM_3:def.6">Def6</a></span>;<br/>
<a NAME="E3:57"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">Q</font> being  <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#K4" title="FSM_3:func.4">_bool</a> <font color="Maroon" title="c3">A</font></span>)</span> st <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Q</font> &amp; <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:57"/>
<font color="Maroon" title="c1">X</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>
 ; <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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