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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b4">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b3">F</font>  st <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Olive" title="b2">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Olive" title="b1">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b4">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Olive" title="b2">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Olive" title="b1">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b4">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">E</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b3">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b2">F</font>  st <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b3">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b3">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">E</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">  for <font color="Olive" title="b1">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b2">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b1">F</font>  st <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b2">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b2">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></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">  for <font color="Olive" title="b1">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Maroon" title="c5">F</font>  st <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b1">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b1">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">TS</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Maroon" title="c5">F</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"> ( <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c6">TS</font> implies <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c6">TS</font> )</span><br/>











<a NAME="E1:16"/>
 not  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <span class="p2">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c6">TS</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#D1" onmouseover="rs('rewrite3/D1')" onmouseout="rh()">REWRITE3:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:16"/>
( <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c6">TS</font> implies <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c2">y</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c3">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c6">TS</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T92" onmouseover="rs('rewrite3/T92')" onmouseout="rh()">REWRITE3:92</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"> verum</span><br/>


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