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

<b>consider </b><font color="Maroon" title="c1">ee</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3</span>)</span></span>)</span><b> such that </b><br/><a NAME="E2:46"/><i><font color="Green" title="E27">A1</font></i>: 
( <font color="Maroon" title="c1">ee</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> where <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  : ( <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Olive" title="b2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">j</font> ) </span>}</span>  &amp;  <a href="sgraph1.html#K8" title="SGRAPH1:func.8">TriangleGraph</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3</span>)</span>,<font color="Maroon" title="c1">ee</font> #) )
 <b>by </b><i><a class="ref" href="sgraph1.html#D17" target="_self" title="SGRAPH1:def.17">Def17</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c1">ee</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">ee</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> &amp;  <a href="sgraph1.html#K8" title="SGRAPH1:func.8">TriangleGraph</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3</span>)</span>,<font color="Maroon" title="c1">ee</font> #) )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">a</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"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> )</span><br/><b>assume </b><a NAME="E1:46_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><b>then consider </b><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:46_1"/><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1_1"/>
( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_1"><b>suppose </b></a><a NAME="E1:46_1_1_1"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1_1_1_1_1"/>
( <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:46_1_1_1_1_1_1"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_1_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_1"><i><font color="Green" title="E29">A3</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="hsNdiv(this)" href="javascript:()" title="46_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:46_1_1_1_1_1_2"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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="hsNdiv(this)" href="javascript:()" title="46_1_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:46_1_1_1_1_1_3"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_1_1_1_3"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:46_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 ; <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="hsNdiv(this)" href="javascript:()" title="46_1_1_2"><b>suppose </b></a><a NAME="E1:46_1_1_2"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1_1_2_1_1"/>
( <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:46_1_1_2_1_1_1"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_2_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_2"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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="hsNdiv(this)" href="javascript:()" title="46_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:46_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_2_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_2"><i><font color="Green" title="E29">A4</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="hsNdiv(this)" href="javascript:()" title="46_1_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:46_1_1_2_1_1_3"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_2_1_1_3"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_2"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:46_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 ; <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="hsNdiv(this)" href="javascript:()" title="46_1_1_3"><b>suppose </b></a><a NAME="E1:46_1_1_3"/><i><font color="Green" title="E29">A5</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1_1_3_1_1"/>
( <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:46_1_1_3_1_1_1"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_3_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_3"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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="hsNdiv(this)" href="javascript:()" title="46_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:46_1_1_3_1_1_2"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_3_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_3"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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="hsNdiv(this)" href="javascript:()" title="46_1_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:46_1_1_3_1_1_3"/>
<font color="Maroon" title="c4">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:46_1_1_3_1_1_3"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 <b>by </b><i><a class="txt" href="#E3:46_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E1:46_1_1_3"><i><font color="Green" title="E29">A5</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><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:46_1_1_3"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 ; <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><b>end;</b></div></div><b>end;</b></div>
<a NAME="E4:46"/><b>then </b><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c1">ee</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">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"> ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font> )</span><br/><b>assume </b><a NAME="E1:46_2"/><i><font color="Green" title="E29">A7</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_2_1"/>
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> or <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> or <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">3,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 </span><b>by </b><i><a class="txt" href="#E1:46_2"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_1"><b>suppose </b></a><a NAME="E1:46_2_1_1"/><i><font color="Green" title="E30">A8</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2_1_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c3">i</font> = 1; <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">j</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">j</font> )</span><br/><b>take </b><font color="Maroon" title="c4">j</font> = 2; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )</span><br/><b>thus </b><a NAME="E1:46_2_1_1_1"/>
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="#E1:46_2_1_1"><i><font color="Green" title="E30">A8</font></i></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="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )</span><br/><b>thus </b><a NAME="E2:46_2_1_1_1"/>
( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 )
 <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</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="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font></span><br/><b>thus </b><a NAME="E3:46_2_1_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font>
 ; <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>hence </b><a NAME="E3:46_2_1_1"/>
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font>
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E27">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="hsNdiv(this)" href="javascript:()" title="46_2_1_2"><b>suppose </b></a><a NAME="E1:46_2_1_2"/><i><font color="Green" title="E30">A9</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2_1_2_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c3">i</font> = 2; <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">j</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">j</font> )</span><br/><b>take </b><font color="Maroon" title="c4">j</font> = 3; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )</span><br/><b>thus </b><a NAME="E1:46_2_1_2_1"/>
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )
 <b>by </b><i><a class="txt" href="#E1:46_2_1_2"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</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>hence </b><a NAME="E3:46_2_1_2"/>
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font>
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E27">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="hsNdiv(this)" href="javascript:()" title="46_2_1_3"><b>suppose </b></a><a NAME="E1:46_2_1_3"/><i><font color="Green" title="E30">A10</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">3,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_2_1_3_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c3">i</font> = 3; <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">j</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Olive" title="b1">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">j</font> )</span><br/><b>take </b><font color="Maroon" title="c4">j</font> = 1; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )</span><br/><b>thus </b><a NAME="E1:46_2_1_3_1"/>
( <font color="Maroon" title="c2">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3 &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">j</font> )
 <b>by </b><i><a class="txt" href="#E1:46_2_1_3"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1" title="FINSEQ_3:th.1">FINSEQ_3:1</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>hence </b><a NAME="E3:46_2_1_3"/>
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">ee</font>
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E27">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><b>end;</b></div></div><b>end;</b></div>
<a NAME="E6:46"/><b>then </b>
<span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">ee</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:46"/>
( <font color="Maroon" title="c1">ee</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="setwiseo.html#K4" title="SETWISEO:func.4">{.</a><span class="default"><span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">1,2</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">2,3</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span>,<span class="p2"><a href="setwiseo.html#K3" title="SETWISEO:func.3">{.</a><span class="default">3,1</span><a href="setwiseo.html#K3" title="SETWISEO:func.3">.}</a></span></span><a href="setwiseo.html#K4" title="SETWISEO:func.4">.}</a></span> &amp;  <a href="sgraph1.html#K8" title="SGRAPH1:func.8">TriangleGraph</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 3</span>)</span>,<font color="Maroon" title="c1">ee</font> #) )
 <b>by </b><i><a class="txt" href="#E2:46"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="#E4:46"><i><font color="Green" title="E28">A6</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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