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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</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="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#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</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="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> <br/>  for <font color="Olive" title="b4">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="catalan2.html#K2" title="CATALAN2:func.2">^omega</a></span>)</span><br/>  for <font color="Olive" title="b5">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 <font color="Olive" title="b4">F</font>  st <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b2">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b5">TS</font> &amp; <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b3">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b5">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<font color="Olive" title="b2">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b5">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a> <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="Maroon" title="c4">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^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> of <font color="Olive" title="b3">F</font>  st <font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b4">TS</font> &amp; <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b2">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b4">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<font color="Olive" title="b1">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b2">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b4">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">u</font>, <font color="Maroon" title="c6">v</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">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="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="c4">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^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> of <font color="Olive" title="b1">F</font>  st <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b2">TS</font> &amp; <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b2">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b2">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">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="c4">E</font> <a href="catalan2.html#K2" title="CATALAN2:func.2">^omega</a></span>)</span>; <a class="txt" 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> of <font color="Maroon" title="c7">F</font>  st <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Olive" title="b1">TS</font> &amp; <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b1">TS</font> holds <br/><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Olive" title="b1">TS</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">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 <font color="Maroon" title="c7">F</font>; <a class="txt" 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>,<font color="Maroon" title="c5">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c8">TS</font> &amp; <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c8">TS</font> implies <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c8">TS</font> )</span><br/>















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:108"/><span class="lab"><font color="Green" title="E86">A1</font></span>: 
<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c8">TS</font>
 <span class="kw">and </span><br/><a NAME="E2:108"/><span class="lab"><font color="Green" title="E87">A2</font></span>: 
<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c8">TS</font>
 ; <a class="txt" 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>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c8">TS</font></span><br/>

<a NAME="E3:108"/>
<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:108"><span class="lab"><font color="Green" title="E86">A1</font></span></a>, <a class="ref" href="rewrite3.html#T96" target="_self" title="REWRITE3:th.96">Th96</a></span>;<br/>
<a NAME="E4:108"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T29" title="AFINSQ_1:th.29">AFINSQ_1:29</a></span>;<br/>
<a NAME="E5:108"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A3</font></span>: 
<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font></span>)</span>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T29" title="AFINSQ_1:th.29">AFINSQ_1:29</a></span>;<br/>
<a NAME="E6:108"/>
<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c3">z</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:108"><span class="lab"><font color="Green" title="E87">A2</font></span></a>, <a class="ref" href="rewrite3.html#D7" target="_self" title="REWRITE3:def.7">Def7</a></span>;<br/>
<a NAME="E7:108"/><span class="kw">then </span>
<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c6">v</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c3">z</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T29" title="AFINSQ_1:th.29">AFINSQ_1:29</a></span>;<br/>
<a NAME="E8:108"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font></span>)</span> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c3">z</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:108"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="ref" href="rewrite3.html#T83" target="_self" title="REWRITE3:th.83">Th83</a></span>;<br/>
<a NAME="E9:108"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c3">z</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c4">E</font>,<font color="Maroon" title="c8">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T29" title="AFINSQ_1:th.29">AFINSQ_1:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:108"/>
<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c6">v</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c3">z</font>,<font color="Maroon" title="c8">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#D7" target="_self" title="REWRITE3:def.7">Def7</a></span>; <a class="txt" 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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