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

<b>reconsider </b><font color="Maroon" title="c1">01</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as  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/>
<b>reconsider </b><font color="Maroon" title="c2">'0</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> , <font color="Maroon" title="c3">'1</font> = 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">01</font> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">'11'</font> = <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">'1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">'1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">01</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">P</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">'0</font>,<font color="Maroon" title="c4">'11'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">01</font>,<font color="Maroon" title="c1">01</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  <b>by </b><i><a class="ref" href="relset_1.html#T8" title="RELSET_1:th.8">RELSET_1:8</a></i>;<br/>
<b>take </b><font color="Maroon" title="c6">cherry</font> =  <a href="lang1.html#G1" title="LANG1:aggr.1">DTConstrStr</a>(# <font color="Maroon" title="c1">01</font>,<font color="Maroon" title="c5">P</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">cherry</font> is <a href="bintree1.html#V3" title="BINTREE1:attr.3">binary</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V1" title="DTCONSTR:attr.1">with_terminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V2" title="DTCONSTR:attr.2">with_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V3" title="DTCONSTR:attr.3">with_useful_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c7">'0</font> = <font color="Maroon" title="c2">'0</font>, <font color="Maroon" title="c8">'1</font> = <font color="Maroon" title="c3">'1</font> as   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> ;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="bintree1.html#D4" target="_self" title="BINTREE1:def.4">BINTREE1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V1" title="DTCONSTR:attr.1">with_terminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V2" title="DTCONSTR:attr.2">with_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V3" title="DTCONSTR:attr.3">with_useful_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a> )</span>
<div class="add"><b>let </b><font color="Maroon" title="c9">s</font> be   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</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">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Maroon" title="c9">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b1">p</font> holds <br/> ex <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c10">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c10">p</font> implies  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> st <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> )</span><br/><b>assume </b><a NAME="E1:17_1_1_1"/>
<font color="Maroon" title="c9">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c10">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> st <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><br/><a NAME="E2:17_1_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">s</font>,<font color="Maroon" title="c10">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 <b>by </b><i><a class="ref" href="lang1.html#D1" title="LANG1:def.1">LANG1:def 1</a></i>;<br/><a NAME="E3:17_1_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">s</font>,<font color="Maroon" title="c10">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">'11'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green" title="E9">A1</font></i>: <font color="Maroon" title="c10">p</font> = 
<font color="Maroon" title="c4">'11'</font>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default">1,1</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D9" title="FINSEQ_1:def.9">FINSEQ_1:def 9</a></i>
;<br/><b>take </b><font color="Maroon" title="c11">x1</font> = <font color="Maroon" title="c8">'1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x2</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> st <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Olive" title="b1">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><br/><b>take </b><font color="Maroon" title="c12">x2</font> = <font color="Maroon" title="c8">'1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span></span><br/><b>thus </b><a NAME="E5:17_1_1_1"/>
<font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="bintree1.html#E4:17_1_1_1"><i><font color="Green" title="E9">A1</font></i></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>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">s</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c8">'1</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c9">s</font></span><br/><b>assume </b><a NAME="E1:17_1_1_2"/>
<font color="Maroon" title="c8">'1</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c9">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:17_1_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c9">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 <b>by </b><i><a class="ref" href="lang1.html#D1" title="LANG1:def.1">LANG1:def 1</a></i>;<br/><a NAME="E3:17_1_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<font color="Maroon" title="c9">s</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">'11'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:17_1_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</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="E8:17_1_1"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c8">'1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t</font> where <font color="Olive" title="b1">t</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> : for <font color="Olive" title="b2">s</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  holds not <font color="Olive" title="b1">t</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">s</font> </span>}</span> 
 
;<br/>
<a NAME="E9:17_1_1"/><b>then </b><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c8">'1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <font color="Maroon" title="c6">cherry</font>
 
<b>by </b><i><a class="ref" href="lang1.html#D2" title="LANG1:def.2">LANG1:def 2</a></i>;<br/>
<b>thus </b><a NAME="E10:17_1_1"/>
 <a href="lang1.html#K5" title="LANG1:func.5">Terminals</a> <font color="Maroon" title="c6">cherry</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="bintree1.html#E8:17_1_1"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="lang1.html#D2" title="LANG1:def.2">LANG1:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="dtconstr.html#D6" title="DTCONSTR:def.6">DTCONSTR:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V2" title="DTCONSTR:attr.2">with_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V3" title="DTCONSTR:attr.3">with_useful_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a> )</span><br/>

<a NAME="E11:17_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">'0</font>,<font color="Maroon" title="c4">'11'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E12:17_1_1"/><b>then </b>
<font color="Maroon" title="c7">'0</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c4">'11'</font>
 
<b>by </b><i><a class="ref" href="lang1.html#D1" title="LANG1:def.1">LANG1:def 1</a></i>;<br/>
<a NAME="E13:17_1_1"/><b>then </b><i><font color="Green" title="E11">A4</font></i>: 
( <font color="Maroon" title="c7">'0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t</font> where <font color="Olive" title="b1">t</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> :  ex <font color="Olive" title="b2">s</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">t</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">s</font> </span>}</span>  &amp; <span class="p1">{<span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> :  ex <font color="Olive" title="b2">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">p</font> </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c6">cherry</font> )
 
<b>by </b><i><a class="ref" href="lang1.html#D3" title="LANG1:def.3">LANG1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E14:17_1_1"/>
 <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c6">cherry</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="dtconstr.html#D7" title="DTCONSTR:def.7">DTCONSTR:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">cherry</font> is <a href="dtconstr.html#V3" title="DTCONSTR:attr.3">with_useful_nonterminals</a> &amp; <font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a> )</span><br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="dtconstr.html#D8" title="DTCONSTR:def.8">DTCONSTR:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a></span>
<div class="add"><b>let </b><font color="Maroon" title="c9">nt</font> be   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">nt</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c6">cherry</font> implies  ex <font color="Olive" title="b1">q'</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Maroon" title="c6">cherry</font> st <font color="Maroon" title="c9">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Olive" title="b1">q'</font> )</span><br/><b>assume </b><a NAME="E1:17_1_1_3"/>
<font color="Maroon" title="c9">nt</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lang1.html#K6" title="LANG1:func.6">NonTerminals</a> <font color="Maroon" title="c6">cherry</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">q'</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Maroon" title="c6">cherry</font> st <font color="Maroon" title="c9">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Olive" title="b1">q'</font></span><br/><a NAME="E2:17_1_1_3"/><b>then </b>
 ex <font color="Olive" title="b1">s</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> st <br/>( <font color="Maroon" title="c9">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp;  ex <font color="Olive" title="b2">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">p</font> )
 <b>by </b><i><a class="txt" href="bintree1.html#E13:17_1_1"><i><font color="Green" title="E11">A4</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c10">p</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E4:17_1_1_3"/><i><font color="Green" title="E12">A5</font></i>: 
<font color="Maroon" title="c9">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c10">p</font>
 ;<br/><a NAME="E5:17_1_1_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">nt</font>,<font color="Maroon" title="c10">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 <b>by </b><i><a class="txt" href="bintree1.html#E4:17_1_1_3"><i><font color="Green" title="E12">A5</font></i></a>, <a class="ref" href="lang1.html#D1" title="LANG1:def.1">LANG1:def 1</a></i>;<br/><a NAME="E6:17_1_1_3"/><b>then </b><i><font color="Green" title="E13">A6</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">nt</font>,<font color="Maroon" title="c10">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></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"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">'11'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">X</font> =  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Maroon" title="c6">cherry</font> as  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>  <b>by </b><i><a class="txt" href="bintree1.html#E9:17_1_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="dtconstr.html#D4" title="DTCONSTR:def.4">DTCONSTR:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">rt1</font> =  <a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Maroon" title="c8">'1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c11">X</font> <b>by </b><i><a class="txt" href="bintree1.html#E9:17_1_1"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="dtconstr.html#D4" title="DTCONSTR:def.4">DTCONSTR:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">q</font> = <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c12">rt1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c12">rt1</font></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> as    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Maroon" title="c6">cherry</font> ;<br/><b>take </b><font color="Maroon" title="c14">q'</font> = <font color="Maroon" title="c13">q</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c14">q'</font></span><br/><a NAME="E10:17_1_1_3"/>
<font color="Maroon" title="c13">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> 1</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D9" title="FINSEQ_1:def.9">FINSEQ_1:def 9</a></i>;<br/><a NAME="E11:17_1_1_3"/><b>then </b>
(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c13">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Maroon" title="c8">'1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Maroon" title="c8">'1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; <font color="Maroon" title="c4">'11'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default">1,1</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; <span class="p1">(<span class="default"><a href="trees_4.html#K1" title="TREES_4:func.1">root-tree</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="ref" href="dtconstr.html#T6" title="DTCONSTR:th.6">DTCONSTR:6</a>, <a class="ref" href="finseq_1.html#D9" title="FINSEQ_1:def.9">FINSEQ_1:def 9</a>, <a class="ref" href="trees_4.html#T3" title="TREES_4:th.3">TREES_4:3</a></i>;<br/><b>hence </b><a NAME="E12:17_1_1_3"/>
<font color="Maroon" title="c9">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c14">q'</font>
 <b>by </b><i><a class="txt" href="bintree1.html#E4:17_1_1_3"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="bintree1.html#E6:17_1_1_3"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</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>

<b>thus </b><a NAME="E16:17_1_1"/>
<font color="Maroon" title="c6">cherry</font> is <a href="lang1.html#V1" title="LANG1:attr.1">strict</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
