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

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:58"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E3:58"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
 <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 class="kw">by</span> <span class="lab"><a class="ref" href="sgraph1.html#D17" target="_self" title="SGRAPH1:def.17">Def17</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c1">ee</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">assume </span><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E3:58_1"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:58_1"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<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
 <span class="kw">and </span><br/><a NAME="E5:58_1"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<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
 <span class="kw">and </span><br/><a NAME="E6:58_1"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E27">A1</font></span></a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58_1"><span class="lab"><font color="Green" title="E30">A4</font></span></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></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_1_1_1"/><span class="lab"><font color="Green" title="E33">A7</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58_1"><span class="lab"><font color="Green" title="E31">A5</font></span></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></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E33">A7</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_1_1_2"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58_1"><span class="lab"><font color="Green" title="E31">A5</font></span></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></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_2"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E1:58_1_1_2"><span class="lab"><font color="Green" title="E33">A8</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_2"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:58_1_1_3"/><span class="lab"><font color="Green" title="E33">A9</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_1_1_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58_1"><span class="lab"><font color="Green" title="E31">A5</font></span></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></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_3"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E1:58_1_1_3"><span class="lab"><font color="Green" title="E33">A9</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_3_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">hence </span><a NAME="E2:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E1:58_1_1_3"><span class="lab"><font color="Green" title="E33">A9</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E5:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A10</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">assume </span><a NAME="E1:58_2"/><span class="lab"><font color="Green" title="E30">A11</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_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><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_2"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_2_1_1"/><span class="lab"><font color="Green" title="E31">A12</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_2_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c3">i</font> = 1; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c4">j</font> = 2; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">thus </span><a NAME="E1:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_2_1_1"><span class="lab"><font color="Green" title="E31">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">thus </span><a NAME="E2:58_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 )
 <span class="kw">by</span> <span class="lab"><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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">thus </span><a NAME="E3:58_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E27">A1</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_2_1_2"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_2_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c3">i</font> = 2; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c4">j</font> = 3; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">thus </span><a NAME="E1:58_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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_2_1_2"><span class="lab"><font color="Green" title="E31">A13</font></span></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></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E27">A1</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:58_2_1_3"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="58_2_1_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">take </span><font color="Maroon" title="c3">i</font> = 3; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c4">j</font> = 1; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">thus </span><a NAME="E1:58_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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_2_1_3"><span class="lab"><font color="Green" title="E31">A14</font></span></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></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/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:58_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E27">A1</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E7:58"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:58"/>
( <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E5:58"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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/>


</div>
