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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">z</font>, <font color="Maroon" title="c4">y2</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">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="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 <font color="Olive" title="b2">F</font>  st <font color="Olive" title="b3">TS</font> is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a>  &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b3">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b3">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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">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="c5">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="Olive" title="b2">TS</font> is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a>  &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b2">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b2">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">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="c5">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="c6">F</font>  st <font color="Olive" title="b1">TS</font> is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a>  &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b1">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Olive" title="b1">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">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="c6">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="c7">TS</font> is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a>  &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp;  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> implies <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> )</span><br/>













<span class="kw">assume </span><a NAME="E1:87"/><span class="lab"><font color="Green" title="E70">A1</font></span>: 
<font color="Maroon" title="c7">TS</font> is  <a href="rewrite3.html#V2" title="REWRITE3:attr.2">deterministic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or  not  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:87"/><span class="lab"><font color="Green" title="E71">A2</font></span>: 
 <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E72">A3</font></span>: 
 <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">x</font>,<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ; <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="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">P</font> being    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font><span class="kw"> such that </span><br/><a NAME="E5:87"/><span class="lab"><font color="Green" title="E73">A4</font></span>: 
<font color="Maroon" title="c8">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">and </span><br/><a NAME="E6:87"/><span class="lab"><font color="Green" title="E74">A5</font></span>: 
<font color="Maroon" title="c8">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">y1</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:87"><span class="lab"><font color="Green" title="E71">A2</font></span></a>, <a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">Q</font> being    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="rewrite3.html#K1" title="REWRITE3:func.1">==&gt;.-relation</a> <font color="Maroon" title="c7">TS</font><span class="kw"> such that </span><br/><a NAME="E8:87"/><span class="lab"><font color="Green" title="E75">A6</font></span>: 
<font color="Maroon" title="c9">Q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">and </span><br/><a NAME="E9:87"/><span class="lab"><font color="Green" title="E76">A7</font></span>: 
<font color="Maroon" title="c9">Q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">y2</font>,<font color="Maroon" title="c3">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E72">A3</font></span></a>, <a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></span>;<br/>
<a NAME="E10:87"/><span class="lab"><font color="Green" title="E77">A8</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">Q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">Q</font></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E76">A7</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E11:87"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">P</font></span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E74">A5</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E12:87"/><span class="kw">then </span>
<font color="Maroon" title="c8">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:87"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="txt" href="#E5:87"><span class="lab"><font color="Green" title="E73">A4</font></span></a>, <a class="txt" href="#E8:87"><span class="lab"><font color="Green" title="E75">A6</font></span></a>, <a class="txt" href="#E10:87"><span class="lab"><font color="Green" title="E77">A8</font></span></a>, <a class="ref" href="rewrite3.html#T69" target="_self" title="REWRITE3:th.69">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:87"/>
<font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:87"><span class="lab"><font color="Green" title="E74">A5</font></span></a>, <a class="txt" href="#E9:87"><span class="lab"><font color="Green" title="E76">A7</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</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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