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

<span class="kw">reconsider </span><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#K5" title="NUMBERS:func.5">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#M2" title="HIDDEN:mode.2">set</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">a90</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> , <font color="Maroon" title="c3">a91</font> = 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">01</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">a9119</font> = <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">a91</font></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">a91</font></span><a href="pre_poly.html#K3" title="PRE_POLY: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/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">P</font> = <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a90</font>,<font color="Maroon" title="c4">a9119</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="lang1.html#K4" title="LANG1:func.4">}</a></span> as   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Maroon" title="c1">01</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">01</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span> ;<br/>
<span class="kw">take </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">a90</font> = <font color="Maroon" title="c2">a90</font>, <font color="Maroon" title="c8">a91</font> = <font color="Maroon" title="c3">a91</font> as   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c6">cherry</font> ;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="bintree1.html#D4" target="_self" onmouseover="rs('bintree1/D4')" onmouseout="rh()">BINTREE1:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">x1</font>,<font color="Olive" title="b3">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c10">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:16_1_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span></span><br/><span class="kw">take </span><font color="Maroon" title="c11">x1</font> = <font color="Maroon" title="c8">a91</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Olive" title="b1">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span></span><br/><span class="kw">take </span><font color="Maroon" title="c12">x2</font> = <font color="Maroon" title="c8">a91</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span></span><br/><a NAME="E2:16_1_1_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="lang1.html#D1" onmouseover="rs('lang1/D1')" onmouseout="rh()">LANG1:def 1</a></span>;<br/><a NAME="E3:16_1_1_1"/><span class="kw">then </span>
<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#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c4">a9119</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><font color="Maroon" title="c10">p</font> = 
<font color="Maroon" title="c4">a9119</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D9" onmouseover="rs('finseq_1/D9')" onmouseout="rh()">FINSEQ_1:def 9</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:16_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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="16_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  holds  not <font color="Maroon" title="c8">a91</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b1">s</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">s</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c8">a91</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c9">s</font></span><br/><span class="kw">assume </span><a NAME="E1:16_1_1_2"/>
<font color="Maroon" title="c8">a91</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c9">s</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:16_1_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D1" onmouseover="rs('lang1/D1')" onmouseout="rh()">LANG1:def 1</a></span>;<br/><a NAME="E3:16_1_1_2"/><span class="kw">then </span>
<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#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c4">a9119</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:16_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E8:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c8">a91</font> <a href="tarski.html#R2" title="TARSKI: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="E9:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A3</font></span>: 
<font color="Maroon" title="c8">a91</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="lang1.html#K1" title="LANG1:func.1">Terminals</a> <font color="Maroon" title="c6">cherry</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D2" onmouseover="rs('lang1/D2')" onmouseout="rh()">LANG1:def 2</a></span>;<br/>
<span class="kw">thus </span><a NAME="E10:16_1_1"/>
 <a href="lang1.html#K1" title="LANG1:func.1">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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16_1_1"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="lang1.html#D2" onmouseover="rs('lang1/D2')" onmouseout="rh()">LANG1:def 2</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="dtconstr.html#D3" onmouseover="rs('dtconstr/D3')" onmouseout="rh()">DTCONSTR:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E11:16_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a90</font>,<font color="Maroon" title="c4">a9119</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E12:16_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a90</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c4">a9119</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D1" onmouseover="rs('lang1/D1')" onmouseout="rh()">LANG1:def 1</a></span>;<br/>
<a NAME="E13:16_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a90</font> <a href="tarski.html#R2" title="TARSKI: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> 
 
;<br/>
<span class="kw">hence </span><a NAME="E14:16_1_1"/>
 <a href="lang1.html#K2" title="LANG1:func.2">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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D3" onmouseover="rs('lang1/D3')" onmouseout="rh()">LANG1:def 3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="dtconstr.html#D4" onmouseover="rs('dtconstr/D4')" onmouseout="rh()">DTCONSTR:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<a NAME="E15:16_1_1"/><span class="lab"><font color="Green" title="E9">A4</font></span>: 
<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#K2" title="LANG1:func.2">NonTerminals</a> <font color="Maroon" title="c6">cherry</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D3" onmouseover="rs('lang1/D3')" onmouseout="rh()">LANG1:def 3</a></span>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="dtconstr.html#D5" onmouseover="rs('dtconstr/D5')" onmouseout="rh()">DTCONSTR:def 5</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">reconsider </span><font color="Maroon" title="c9">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#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16_1_1"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="dtconstr.html#D1" onmouseover="rs('dtconstr/D1')" onmouseout="rh()">DTCONSTR:def 1</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c10">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">nt</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="lang1.html#K2" title="LANG1:func.2">NonTerminals</a> <font color="Maroon" title="c6">cherry</font> implies  ex <font color="Olive" title="b1">q9</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="c10">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">q9</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c11">rt1</font> =  <a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Maroon" title="c8">a91</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16_1_1"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="dtconstr.html#D1" onmouseover="rs('dtconstr/D1')" onmouseout="rh()">DTCONSTR:def 1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">q</font> = <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c11">rt1</font></span><a href="pre_poly.html#K3" title="PRE_POLY:func.3">*&gt;</a></span> <a href="pre_poly.html#K1" title="PRE_POLY:func.1">^</a> <span class="p1"><a href="pre_poly.html#K3" title="PRE_POLY:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c11">rt1</font></span><a href="pre_poly.html#K3" title="PRE_POLY: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/><a NAME="E4:16_1_1_3"/>
<font color="Maroon" title="c12">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D9" onmouseover="rs('finseq_1/D9')" onmouseout="rh()">FINSEQ_1:def 9</a></span>;<br/><a NAME="E5:16_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A5</font></span>: 
 <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c12">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">a91</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">a91</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="dtconstr.html#T6" onmouseover="rs('dtconstr/T6')" onmouseout="rh()">DTCONSTR:6</a></span>;<br/><span class="kw">assume </span><a NAME="E6:16_1_1_3"/>
<font color="Maroon" title="c10">nt</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="lang1.html#K2" title="LANG1:func.2">NonTerminals</a> <font color="Maroon" title="c6">cherry</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">q9</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="c10">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">q9</font></span><br/><a NAME="E7:16_1_1_3"/><span class="kw">then </span>
 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="c10">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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:16_1_1"><span class="lab"><font color="Green" title="E9">A4</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">p</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E9:16_1_1_3"/><span class="lab"><font color="Green" title="E11">A6</font></span>: 
<font color="Maroon" title="c10">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Maroon" title="c13">p</font>
 ;<br/><span class="kw">take </span><font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">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">q9</font></span><br/><a NAME="E10:16_1_1_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">nt</font>,<font color="Maroon" title="c13">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16_1_1_3"><span class="lab"><font color="Green" title="E11">A6</font></span></a>, <a class="ref" href="lang1.html#D1" onmouseover="rs('lang1/D1')" onmouseout="rh()">LANG1:def 1</a></span>;<br/><a NAME="E11:16_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A7</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">nt</font>,<font color="Maroon" title="c13">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#K5" title="NUMBERS:func.5">0</a>,<font color="Maroon" title="c4">a9119</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/><a NAME="E12:16_1_1_3"/>
( <font color="Maroon" title="c4">a9119</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 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D9" onmouseover="rs('finseq_1/D9')" onmouseout="rh()">FINSEQ_1:def 9</a>, <a class="ref" href="trees_4.html#T3" onmouseover="rs('trees_4/T3')" onmouseout="rh()">TREES_4:3</a></span>;<br/><span class="kw">hence </span><a NAME="E13:16_1_1_3"/>
<font color="Maroon" title="c10">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">q9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16_1_1_3"><span class="lab"><font color="Green" title="E11">A6</font></span></a>, <a class="txt" href="#E11:16_1_1_3"><span class="lab"><font color="Green" title="E12">A7</font></span></a>, <a class="txt" href="#E5:16_1_1_3"><span class="lab"><font color="Green" title="E10">A5</font></span></a>, <a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E17:16_1_1"/>
<font color="Maroon" title="c6">cherry</font> is  <a href="lang1.html#V1" title="LANG1:attr.1">strict</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
