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

<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="modal_1.html#NM1" title="MODAL_1:NM.1">MP-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="modal_1.html#NM5" title="MODAL_1:NM.5">MP-wff</a> holds <br/> (  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K10" title="MODAL_1:func.10">'not'</a> <font color="Olive" title="b1">A</font> &amp;  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Olive" title="b1">A</font> &amp;  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Olive" title="b2">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="modal_1.html#NM5" title="MODAL_1:NM.5">MP-wff</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K10" title="MODAL_1:func.10">'not'</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">e2</font> =  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">e1</font> =  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">e0</font> =  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<a NAME="E1:69"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E2:69"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a>, <a class="ref" href="trees_1.html#T88" title="TREES_1:th.88">TREES_1:88</a></span>;<br/>
<a NAME="E3:69"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E4:69"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="modal_1.html#K10" title="MODAL_1:func.10">'not'</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="trees_2.html#D12" title="TREES_2:def.12">TREES_2:def 12</a></span>;<br/>
<a NAME="E5:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="modal_1.html#K10" title="MODAL_1:func.10">'not'</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="trees_1.html#D12" title="TREES_1:def.12">TREES_1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:69"/>
 <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K10" title="MODAL_1:func.10">'not'</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="trees_1.html#T56" title="TREES_1:th.56">TREES_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<a NAME="E7:69"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E8:69"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 1</span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="trees_2.html#D12" title="TREES_2:def.12">TREES_2:def 12</a></span>;<br/>
<a NAME="E9:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="trees_1.html#D12" title="TREES_1:def.12">TREES_1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:69"/>
 <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="modal_1.html#K11" title="MODAL_1:func.11">(#)</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="trees_1.html#T56" title="TREES_1:th.56">TREES_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">y</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_2.html#K8" title="TREES_2:func.8">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<font color="Maroon" title="c2">A</font>;<br/>
<a NAME="E11:69"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2 &amp; not <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_1.html#T55" title="TREES_1:th.55">TREES_1:55</a>, <a class="ref" href="trees_1.html#T89" title="TREES_1:th.89">TREES_1:89</a></span>;<br/>
<a NAME="E12:69"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
( <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2 &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a>, <a class="ref" href="trees_1.html#T55" title="TREES_1:th.55">TREES_1:55</a></span>;<br/>
<a NAME="E13:69"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_2.html#K8" title="TREES_2:func.8">with-replacement</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span></span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_2.html#D12" title="TREES_2:def.12">TREES_2:def 12</a></span>;<br/>
<a NAME="E14:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_2.html#K8" title="TREES_2:func.8">with-replacement</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:69"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E11:69"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="trees_1.html#D12" title="TREES_1:def.12">TREES_1:def 12</a></span>;<br/>
<a NAME="E15:69"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="trees_1.html#K2" title="TREES_1:func.2">elementary_tree</a> 2</span>)</span> <a href="trees_2.html#K9" title="TREES_2:func.9">--&gt;</a> <span class="p4"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> <a href="trees_2.html#K8" title="TREES_2:func.8">with-replacement</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_2.html#D12" title="TREES_2:def.12">TREES_2:def 12</a></span>;<br/>
<a NAME="E16:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:69"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="ref" href="trees_1.html#D12" title="TREES_1:def.12">TREES_1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:69"/>
 <a href="modal_1.html#K16" title="MODAL_1:func.16">@</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">A</font> <a href="modal_1.html#K12" title="MODAL_1:func.12">'&amp;'</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="trees_1.html#T56" title="TREES_1:th.56">TREES_1:56</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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