<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="rewrite2.html#NM1" title="REWRITE2:NM.1">semi-Thue-system</a> of <font color="Maroon" title="c1">E</font><br/> for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font>, <font color="Olive" title="b4">u</font> being   <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a>   st <font color="Olive" title="b2">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b3">t</font>,<font color="Olive" title="b1">S</font> holds <br/>( <font color="Olive" title="b2">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b4">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b3">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b4">u</font>,<font color="Olive" title="b1">S</font> &amp; <font color="Olive" title="b4">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b2">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b4">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">t</font>,<font color="Olive" title="b1">S</font> )</span><br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="rewrite2.html#NM1" title="REWRITE2:NM.1">semi-Thue-system</a> of <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font>, <font color="Olive" title="b3">u</font> being   <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a>   st <font color="Olive" title="b1">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b2">t</font>,<font color="Maroon" title="c2">S</font> holds <br/>( <font color="Olive" title="b1">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b2">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b3">u</font>,<font color="Maroon" title="c2">S</font> &amp; <font color="Olive" title="b3">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b1">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Olive" title="b3">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Olive" title="b2">t</font>,<font color="Maroon" title="c2">S</font> )</span><br/><b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c5">u</font> be    <a href="catalan2.html#M2" title="CATALAN2:mode.2">Element</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font> implies ( <font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font> ) )</span><br/>









<b>assume </b><a NAME="E1:56"/>
<font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">S</font> &amp; <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font> )</span><br/>

<a NAME="E2:56"/><b>then </b>
 <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#D7" target="_self" title="REWRITE2:def.7">Def7</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">p</font> being    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E4:56"/><i><font color="Green" title="E37">A1</font></i>: 
( <font color="Maroon" title="c6">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="c3">s</font> &amp; <font color="Maroon" title="c6">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="c6">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> )
 <b>by </b><i><a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">p</font> = <font color="Maroon" title="c6">p</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a>  <b>by </b><i><a class="txt" href="#E4:56"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="abcmiz_0.html#T74" title="ABCMIZ_0:th.74">ABCMIZ_0:74</a></i>;<br/>
<a NAME="E6:56"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font> is    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T23" target="_self" title="REWRITE2:th.23">Th23</a></i>;<br/>
<a NAME="E7:56"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>proof </b></a><div class="add">

<a NAME="E1:56_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></i>;<br/>
<b>hence </b><a NAME="E2:56_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>
 <b>by </b><i><a class="txt" href="#E4:56"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="rewrite2.html#D3" target="_self" title="REWRITE2:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font></span><br/>

<a NAME="E3:56_1"/><i><font color="Green" title="E39">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T5" target="_self" title="REWRITE2:th.5">Th5</a></i>;<br/>
<a NAME="E4:56_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></i>;<br/>
<b>hence </b><a NAME="E5:56_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="rewrite2.html#K7" title="REWRITE2:func.7">+^</a> <font color="Maroon" title="c5">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>
 <b>by </b><i><a class="txt" href="#E4:56"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="#E3:56_1"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="rewrite2.html#D3" target="_self" title="REWRITE2:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:56"/><b>then </b>
 <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>
 
<b>by </b><i><a class="txt" href="#E6:56"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:56"/>
<font color="Maroon" title="c3">s</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c4">t</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="rewrite2.html#D7" target="_self" title="REWRITE2:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font></span><br/>

<a NAME="E10:56"/><i><font color="Green" title="E39">A4</font></i>: 
<font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font> is    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of  <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T23" target="_self" title="REWRITE2:th.23">Th23</a></i>;<br/>
<a NAME="E11:56"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_2"><b>proof </b></a><div class="add">

<a NAME="E1:56_2"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></i>;<br/>
<b>hence </b><a NAME="E2:56_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="txt" href="#E4:56"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font></span><br/>

<a NAME="E3:56_2"/><i><font color="Green" title="E40">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rewrite2.html#T5" target="_self" title="REWRITE2:th.5">Th5</a></i>;<br/>
<a NAME="E4:56_2"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T6" title="FINSEQ_5:th.6">FINSEQ_5:6</a></i>;<br/>
<b>hence </b><a NAME="E5:56_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="rewrite2.html#K4" title="REWRITE2:func.4">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">u</font> <a href="rewrite2.html#K6" title="REWRITE2:func.6">^+</a> <font color="Maroon" title="c7">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>
 <b>by </b><i><a class="txt" href="#E4:56"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="#E3:56_2"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E12:56"/><b>then </b>
 <a href="rewrite2.html#K9" title="REWRITE2:func.9">==&gt;.-relation</a> <font color="Maroon" title="c2">S</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>
 
<b>by </b><i><a class="txt" href="#E10:56"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="rewrite1.html#D3" title="REWRITE1:def.3">REWRITE1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E13:56"/>
<font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c3">s</font> <a href="rewrite2.html#R3" title="REWRITE2:pred.3">==&gt;*</a> <font color="Maroon" title="c5">u</font> <a href="flang_1.html#K1" title="FLANG_1:func.1">^</a> <font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="rewrite2.html#D7" target="_self" title="REWRITE2:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
