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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">w</font>, <font color="Olive" title="b3">v</font> being   <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Olive" title="b1">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> <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> 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> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">v</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="b4">TS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="b4">TS</font></span>)</span>,<font color="Olive" title="b4">TS</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">w</font>, <font color="Olive" title="b2">v</font> being   <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c2">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> <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> 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> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b2">v</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">TS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="b3">TS</font></span>)</span>,<font color="Olive" title="b3">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">w</font>, <font color="Maroon" title="c4">v</font> be    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c2">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</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">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> 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> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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">TS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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">TS</font></span>)</span>,<font color="Olive" title="b1">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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> 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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font></span><br/>









<div><span class="lab"><font color="Green" title="E33">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font> implies <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font> )</span><br/><span class="kw">assume </span><a NAME="E1:52_1"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">r</font> = <font color="Maroon" title="c6">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c8">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font><span class="kw"> such that </span><br/><a NAME="E4:52_1"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
<font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c5">TS</font>
 <span class="kw">and </span><br/><a NAME="E5:52_1"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c4">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font><span class="kw"> such that </span><br/><a NAME="E7:52_1"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon" title="c9">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E8:52_1"/><span class="lab"><font color="Green" title="E38">A6</font></span>: 
<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</a></span>;<br/><a NAME="E9:52_1"/>
<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="txt" href="#E8:52_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="ref" href="rewrite3.html#T99" title="REWRITE3:th.99">REWRITE3:99</a></span>;<br/><span class="kw">hence </span><a NAME="E10:52_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:52_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</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/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font> implies <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font> )</span><br/><span class="kw">assume </span><a NAME="E1:52_2"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">r</font> = <font color="Maroon" title="c6">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font> ;<br/><span class="kw">consider </span><font color="Maroon" title="c8">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font><span class="kw"> such that </span><br/><a NAME="E4:52_2"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E5:52_2"/><span class="lab"><font color="Green" title="E36">A9</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c9">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">TS</font><span class="kw"> such that </span><br/><a NAME="E7:52_2"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">and </span><br/><a NAME="E8:52_2"/><span class="lab"><font color="Green" title="E38">A11</font></span>: 
<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c4">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52_2"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="fsm_3.html#T29" target="_self" title="FSM_3:th.29">Th29</a></span>;<br/><a NAME="E9:52_2"/>
<font color="Maroon" title="c9">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <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="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E7:52_2"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</a></span>;<br/><span class="kw">hence </span><a NAME="E10:52_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="rewrite3.html#T103" title="REWRITE3:th.103">REWRITE3:103</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:52"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">v</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="c5">TS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> <span class="p1">(<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="c5">TS</font></span>)</span>,<font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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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