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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">v</font>, <font color="Olive" title="b3">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="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 <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="b3">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="b4">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="b3">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#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">v</font>, <font color="Olive" title="b2">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="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 <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="b2">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b1">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="b1">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="b3">TS</font>)</span>)</span>,<font color="Olive" title="b3">TS</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">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">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 <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="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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> 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"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="51_1"><span class="kw">now </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">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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>) holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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></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">object</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"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="E1:51_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="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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" 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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="E4:51_1"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
<font color="Maroon" title="c8">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">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="E5:51_1"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c3">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="#E1:51_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">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="E7:51_1"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon" title="c9">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E8:51_1"/><span class="lab"><font color="Green" title="E38">A6</font></span>: 
<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c4">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="#E4:51_1"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">REWRITE3:103</a></span>;<br/><a NAME="E9:51_1"/>
<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="#E5:51_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="txt" href="#E8:51_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="ref" href="rewrite3.html#T99" onmouseover="rs('rewrite3/T99')" onmouseout="rh()">REWRITE3:99</a></span>;<br/><span class="kw">hence </span><a NAME="E10:51_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="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="#E7:51_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">REWRITE3:103</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/></div><span class="kw">end;</span></div>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="51_2"><span class="kw">now </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">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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>) holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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></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">object</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"> ( <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="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="E1:51_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="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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" 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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="E4:51_2"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E5:51_2"/><span class="lab"><font color="Green" title="E36">A9</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="#E1:51_2"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">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="E7:51_2"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<font color="Maroon" title="c8">q</font>,<font color="Maroon" title="c4">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="E8:51_2"/><span class="lab"><font color="Green" title="E38">A11</font></span>: 
<font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c3">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="#E5:51_2"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="ref" href="fsm_3.html#T28" target="_self" onmouseover="rs('fsm_3/T28')" onmouseout="rh()">Th28</a></span>;<br/><a NAME="E9:51_2"/>
<font color="Maroon" title="c9">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">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="#E4:51_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E7:51_2"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">REWRITE3:103</a></span>;<br/><span class="kw">hence </span><a NAME="E10:51_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="#E8:51_2"><span class="lab"><font color="Green" title="E38">A11</font></span></a>, <a class="ref" href="rewrite3.html#T103" onmouseover="rs('rewrite3/T103')" onmouseout="rh()">REWRITE3:103</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:51"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">w</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">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="c3">v</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="#E1:51"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="tarski.html#T2" onmouseover="rs('tarski/T2')" onmouseout="rh()">TARSKI:2</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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