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

<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:9_1"/><i><font color="Green" title="E8">A1</font></i>: 
not <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font>
 ;<br/><div><i><font color="Green" title="E9">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font>
 ;<br/><a NAME="E2:9_1_1"/><b>then </b><i><font color="Green" title="E10">A3</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:9_1_1"/>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></i>;<br/><a NAME="E4:9_1_1"/><b>then </b>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="helly.html#E2:9_1_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="grfunc_1.html#T9" title="GRFUNC_1:th.9">GRFUNC_1:9</a></i>;<br/><b>hence </b><a NAME="E5:9_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="helly.html#E1:9_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></i>;<br/></div><b>end;</b></div><a NAME="E3:9_1"/>
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></i>;<br/><a NAME="E4:9_1"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T84" title="FINSEQ_1:th.84">FINSEQ_1:84</a></i>;<br/><b>hence </b><a NAME="E5:9_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="helly.html#E2:9_1"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><b>that </b><br/><a NAME="E2:9"/><i><font color="Green" title="E8">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">p</font>
 <b>and </b><br/><a NAME="E3:9"/><i><font color="Green" title="E9">A5</font></i>: 
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">q</font>
 ;<br/>

<a NAME="E4:9"/><i><font color="Green" title="E10">A6</font></i>: 
 <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></i>;<br/>
<a NAME="E5:9"/>
<font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="txt" href="helly.html#E3:9"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="helly.html#D1" target="_self" title="HELLY:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E6:9"/>
contradiction
 <b>by </b><i><a class="txt" href="helly.html#E2:9"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="helly.html#E4:9"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
