Sindbad~EG File Manager
TRABC
EAABHHBC
EABCJJCA
BEAHC
BEAJB
BECHA axiom:betweennesssymmetry
NCABC defn:triangle
NCCAB lemma:NCorder
BEBJA axiom:betweennesssymmetry
ANBECDJ+BEBDH postulate:Pasch-inner
BECDJ
BEBDH
COABH assumption
COHAB lemma:collinearorder
COAHC defn:collinear
COHAC lemma:collinearorder
NEAH lemma:betweennotequal
NEHA lemma:inequalitysymmetric
COABC lemma:collinear4
NCABH reductio
EAABHABH lemma:equalanglesreflexive
NEBH lemma:betweennotequal
NEAB lemma:NCdistinct
NEBA lemma:inequalitysymmetric
RABHD lemma:ray4
EQAA cn:equalityreflexive
RABAA lemma:ray4
EAABHABD lemma:equalangleshelper
NCABD lemma:equalanglesNC
COBCJ assumption
COJBC lemma:collinearorder
COAJB defn:collinear
COJBA lemma:collinearorder
NEJB lemma:betweennotequal
COBCA lemma:collinear4
COABC lemma:collinearorder
NCBCJ reductio
EABCJBCJ lemma:equalanglesreflexive
NECJ lemma:NCdistinct
NECD lemma:betweennotequal
RACJD lemma:ray4
NECA lemma:NCdistinct
EQBB cn:equalityreflexive
NECB lemma:NCdistinct
RACBB lemma:ray4
EABCJBCD lemma:equalangleshelper
NCBCD lemma:equalanglesNC
NCABC defn:triangle
NCBCA lemma:NCorder
NEDH lemma:betweennotequal
NEHD lemma:inequalitysymmetric
BEHDB axiom:betweennesssymmetry
COHDB defn:collinear
CODHB lemma:collinearorder
COAHC defn:collinear
COACH lemma:collinearorder
NEAC lemma:betweennotequal
COACD assumption
COCHD lemma:collinear4
CODHC lemma:collinearorder
NEDH lemma:betweennotequal
COHBC lemma:collinear4
COHCB lemma:collinearorder
COHCA lemma:collinearorder
NEHC lemma:betweennotequal
COCBA lemma:collinear4
COABC lemma:collinearorder
NCACD reductio
NEBC lemma:NCdistinct
NCCJB lemma:NCorder
EQCC cn:equalityreflexive
COCJC defn:collinear
COCDJ defn:collinear
COCJD lemma:collinearorder
NEDJ lemma:betweennotequal
NEJD lemma:inequalitysymmetric
NECD lemma:betweennotequal
NCCDB lemma:NChelper
NCBCD lemma:NCorder
PADFBCF proposition:12
ANCODFF+COBCF+COBCP+RRPFD defn:perpat
COBCF
COBCP
RRPFD
NCCBD lemma:NCorder
EACBDCBD lemma:equalanglesreflexive
EQCC cn:equalityreflexive
RABCC lemma:ray4
NEBD lemma:betweennotequal
RABDH lemma:ray4
EACBDCBH lemma:equalangleshelper
EQHH cn:equalityreflexive
COBHH defn:collinear
NCBHA lemma:NCorder
OSABHC defn:oppositeside
OSCBHA lemma:oppositesidesymmetric
EQBF assumption
RRPBD cn:equalitysub
RRDBP lemma:8.2
NEBP defn:rightangle
NEPB lemma:inequalitysymmetric
COPBC lemma:collinearorder
RRCBD lemma:collinearright
EACBHCBD lemma:equalanglessymmetric
RRCBH lemma:equaltorightisright
RRHBC lemma:8.2
EAHBCABH lemma:equalanglessymmetric
RRABH lemma:equaltorightisright
BEABC lemma:rightcollinear
COABC defn:collinear
NEBF reductio
COCBP lemma:collinearorder
COCBF lemma:collinearorder
COBPF lemma:collinear4
COPFB lemma:collinearorder
RRBFD lemma:collinearright
NCBFD lemma:rightangleNC
NCBAD lemma:NCorder
PADEBAE proposition:12
ANCODEE+COBAE+COBAQ+RRQED defn:perpat
COBAE
COBAQ
RRQED
NCABD lemma:NCorder
EAABDABD lemma:equalanglesreflexive
EQAA cn:equalityreflexive
RABAA lemma:ray4
EAABDABH lemma:equalangleshelper
EQBE assumption
RRQBD cn:equalitysub
RRDBQ lemma:8.2
NEBQ defn:rightangle
NEQB lemma:inequalitysymmetric
COQBA lemma:collinearorder
RRABD lemma:collinearright
EAABHABD lemma:equalanglessymmetric
RRABH lemma:equaltorightisright
RRHBA lemma:8.2
EAHBACBH lemma:equalanglesflip
EACBHHBA lemma:equalanglessymmetric
RRCBH lemma:equaltorightisright
BECBA lemma:rightcollinear
COCBA defn:collinear
COABC lemma:collinearorder
NEBE reductio
COABQ lemma:collinearorder
COABE lemma:collinearorder
COBQE lemma:collinear4
COQEB lemma:collinearorder
RRBED lemma:collinearright
EQBB cn:equalityreflexive
COBEB defn:collinear
RRBED lemma:collinearright
NCBED lemma:rightangleNC
EABEDBFD lemma:Euclid4
EEBDBD cn:congruencereflexive
NCBED lemma:rightangleNC
NCDBE lemma:NCorder
TRDBE defn:triangle
NCBFD lemma:rightangleNC
NCDBF lemma:NCorder
TRDBF defn:triangle
RABHD lemma:ray4
COBFC lemma:collinearorder
NCDBC lemma:NCorder
BECDJ
NCCBJ lemma:NCorder
EAABHHBC
EAHBCABH lemma:equalanglessymmetric
EAABHABH lemma:equalanglesreflexive
RABAJ lemma:ray4
RABHD lemma:ray4
EAABHJBD lemma:equalangleshelper
COJBD assumption
CODJB lemma:collinearorder
CODJC lemma:collinearorder
NEJB lemma:betweennotequal
COJBC lemma:collinear4
COCBJ lemma:collinearorder
NCJBD reductio
EAJBDDBJ lemma:ABCequalsCBA
EAABHDBJ lemma:equalanglestransitive
COHBC assumption
COHCB lemma:collinearorder
COAHC defn:collinear
COHCA lemma:collinearorder
NEHC lemma:betweennotequal
COCBA lemma:collinear4
COABC lemma:collinearorder
NCHBC reductio
EAHBCHBC lemma:equalanglesreflexive
RABHD
EQCC cn:equalityreflexive
RABCC lemma:ray4
EAHBCDBC lemma:equalangleshelper
EADBCHBC lemma:equalanglessymmetric
NCCBD
EACBDDBC lemma:ABCequalsCBA
EACBDHBC lemma:equalanglestransitive
NCDBC
EADBCCBD lemma:ABCequalsCBA
EAHBCCBD lemma:equalanglestransitive
EADBJABH lemma:equalanglessymmetric
EACBDABH lemma:equalanglestransitive
EACBDDBJ lemma:equalanglestransitive
AOCBDBFD lemma:halfanglelessthanright
EADBCCBD lemma:ABCequalsCBA
AODBCBFD lemma:angleorderrespectscongruence2
RRDFB lemma:8.2
RABFC lemma:acutebetween
RABCF lemma:ray5
EAABHDBF lemma:equalangleshelper
EADBFABH lemma:equalanglessymmetric
EQAA cn:equalityreflexive
RABAA lemma:ray4
COHBA assumption
COHAB lemma:collinearorder
COAHC defn:collinear
COHAC lemma:collinearorder
NEAH lemma:betweennotequal
NEHA lemma:inequalitysymmetric
COABC lemma:collinear4
NCHBA reductio
EAHBAHBA lemma:equalanglesreflexive
EAHBADBA lemma:equalangleshelper
EADBAHBA lemma:equalanglessymmetric
EAHBAABH lemma:ABCequalsCBA
EADBAABH lemma:equalanglestransitive
NCABD
EAABDDBA lemma:ABCequalsCBA
EAABDHBA lemma:equalanglestransitive
NCDBA lemma:NCorder
EADBAABD lemma:ABCequalsCBA
EAHBAABD lemma:equalanglestransitive
RRDEB lemma:8.2
COBEA lemma:collinearorder
AOABHBED lemma:halfanglelessthanright
AODBABED lemma:angleorderrespectscongruence2
NCABH lemma:NCorder
RABEA lemma:acutebetween
RABAE lemma:ray5
RABHD lemma:ray4
EADBFEBD lemma:equalangleshelper
NCDEB lemma:rightangleNC
NCEBD lemma:NCorder
EAEBDDBE lemma:ABCequalsCBA
EADBFDBE lemma:equalanglestransitive
EABFDBED lemma:equalanglessymmetric
TRDBF defn:triangle
TRDBE defn:triangle
EEDBDB cn:congruencereflexive
EEDFDE proposition:26B
EEBFBE proposition:26B
PADGACG proposition:12
ANCODGG+COACG+COACS+RRSGD defn:perpat
COACG
COACS
RRSGD
NCACD
EQAA cn:equalityreflexive
RACAA lemma:ray4
RACDJ lemma:ray4
EAACDACD lemma:equalanglesreflexive
EAACDACJ lemma:equalangleshelper
BEBJA axiom:betweennesssymmetry
EQJJ cn:equalityreflexive
COCJJ defn:collinear
NCCJB
OSBCJA defn:oppositeside
EQCG assumption
RRSCD cn:equalitysub
RRDCS lemma:8.2
NECS defn:rightangle
NESC lemma:inequalitysymmetric
COSCA lemma:collinearorder
RRACD lemma:collinearright
EAACJACD lemma:equalanglessymmetric
RRACJ lemma:equaltorightisright
RRJCA lemma:8.2
EABCJJCA
RRBCJ lemma:equaltorightisright
RRJCB lemma:8.2
BEBCA lemma:rightcollinear
COBCA defn:collinear
COABC lemma:collinearorder
NECG reductio
COACG
COACS
NEAC
COCGS lemma:collinear4
COSGC lemma:collinearorder
RRCGD lemma:collinearright
EQCC cn:equalityreflexive
COCGC defn:collinear
RRCGD lemma:collinearright
NCCGD lemma:rightangleNC
RRBFD
COBFC
COCBF lemma:collinearorder
COCBP lemma:collinearorder
NCBCD lemma:NCorder
EABCDBCD lemma:equalanglesreflexive
EQBB cn:equalityreflexive
RACBB lemma:ray4
NECD lemma:betweennotequal
RACDJ lemma:ray4
EABCDBCJ lemma:equalangleshelper
EQJJ cn:equalityreflexive
COCJJ defn:collinear
COCJA assumption
COJAC lemma:collinearorder
COAJB defn:collinear
COJAB lemma:collinearorder
NEAJ lemma:betweennotequal
NEJA lemma:inequalitysymmetric
COACB lemma:collinear4
COABC lemma:collinearorder
NCCJA reductio
OSACJB defn:oppositeside
OSBCJA lemma:oppositesidesymmetric
EQCF assumption
RRPCD cn:equalitysub
RRDCP lemma:8.2
NECP defn:rightangle
NEPC lemma:inequalitysymmetric
COPCB lemma:collinearorder
RRBCD lemma:collinearright
EABCJBCD lemma:equalanglessymmetric
RRBCJ lemma:equaltorightisright
RRJCB lemma:8.2
EABCJJCA
EAJCABCJ lemma:equalanglessymmetric
RRJCA lemma:equaltorightisright
RRACJ lemma:8.2
BEACB lemma:rightcollinear
COACB defn:collinear
COABC lemma:collinearorder
NECF reductio
RRCFD lemma:collinearright
EACGDCFD lemma:Euclid4
EECDCD cn:congruencereflexive
NCCGD lemma:rightangleNC
NCDCG lemma:NCorder
TRDCG defn:triangle
NCCGD lemma:rightangleNC
NCDCG lemma:NCorder
%TRDCF defn:triangle
RACJD lemma:ray4
COCFB lemma:collinearorder
NCDCB lemma:NCorder
BECDJ
NCBCJ lemma:NCorder
EAJCBACJ lemma:equalanglesflip
EAACJJCB lemma:equalanglessymmetric
EAJCBACJ lemma:equalanglessymmetric
COACJ assumption
COJAC lemma:collinearorder
COAJB defn:collinear
COJAB lemma:collinearorder
NEAJ lemma:betweennotequal
NEJA lemma:inequalitysymmetric
COACB lemma:collinear4
COABC lemma:collinearorder
NCACJ reductio
EAACJACJ lemma:equalanglesreflexive
RACAH lemma:ray4
RACJD lemma:ray4
EAACJHCD lemma:equalangleshelper
COHCD assumption
CODHC lemma:collinearorder
CODHB lemma:collinearorder
NEHC lemma:betweennotequal
COHCB lemma:collinear4
COAHC defn:collinear
COHCA lemma:collinearorder
NEHC lemma:betweennotequal
COCBA lemma:collinear4
COABC lemma:collinearorder
NCHCD reductio
EAHCDDCH lemma:ABCequalsCBA
EAACJDCH lemma:equalanglestransitive
COJCB assumption
COJBC lemma:collinearorder
COAJB defn:collinear
COJBA lemma:collinearorder
NEJB lemma:betweennotequal
COBCA lemma:collinear4
COABC lemma:collinearorder
NCJCB reductio
EAJCBJCB lemma:equalanglesreflexive
RACJD
EQBB cn:equalityreflexive
RACBB lemma:ray4
EAJCBDCB lemma:equalangleshelper
EADCBJCB lemma:equalanglessymmetric
NCBCD
EABCDDCB lemma:ABCequalsCBA
EABCDJCB lemma:equalanglestransitive
NCDCB
EADCBBCD lemma:ABCequalsCBA
EAJCBBCD lemma:equalanglestransitive
EADCHACJ lemma:equalanglessymmetric
EABCDACJ lemma:equalanglestransitive
EABCDDCH lemma:equalanglestransitive
COBCH assumption
COAHC defn:collinear
COHCA lemma:collinearorder
COHCB lemma:collinearorder
NEHC lemma:betweennotequal
COCAB lemma:collinear4
COABC lemma:collinearorder
NCBCH reductio
RRCFD
BEBDH
AOBCDCFD lemma:halfanglelessthanright
EADCBBCD lemma:ABCequalsCBA
AODCBCFD lemma:angleorderrespectscongruence2
RRDFC lemma:8.2
RACFB lemma:acutebetween
RACBF lemma:ray5
EAACJDCF lemma:equalangleshelper
EADCFACJ lemma:equalanglessymmetric
EQAA cn:equalityreflexive
RACAA lemma:ray4
COJCA assumption
COJAC lemma:collinearorder
COAJB defn:collinear
COJAB lemma:collinearorder
NEAJ lemma:betweennotequal
NEJA lemma:inequalitysymmetric
COACB lemma:collinear4
COABC lemma:collinearorder
NCJCA reductio
EAJCAJCA lemma:equalanglesreflexive
EAJCADCA lemma:equalangleshelper
EADCAJCA lemma:equalanglessymmetric
EAJCAACJ lemma:ABCequalsCBA
EADCAACJ lemma:equalanglestransitive
NCACD
EAACDDCA lemma:ABCequalsCBA
EAACDJCA lemma:equalanglestransitive
NCDCA lemma:NCorder
EADCAACD lemma:ABCequalsCBA
EAJCAACD lemma:equalanglestransitive
RRDGC lemma:8.2
COCGA lemma:collinearorder
BEAJB
NCACB lemma:NCorder
RRCGD
EAACJJCB
AOACJCGD lemma:halfanglelessthanright
AODCACGD lemma:angleorderrespectscongruence2
NCACJ lemma:NCorder
RACGA lemma:acutebetween
RACAG lemma:ray5
RACJD lemma:ray4
EADCFGCD lemma:equalangleshelper
NCDGC lemma:rightangleNC
NCGCD lemma:NCorder
EAGCDDCG lemma:ABCequalsCBA
EADCFDCG lemma:equalanglestransitive
EACFDCGD lemma:equalanglessymmetric
NCCFD lemma:equalanglesNC
NCDCF lemma:NCorder
TRDCF defn:triangle
EADCGDCF lemma:equalanglessymmetric
NCDCG lemma:equalanglesNC
TRDCG defn:triangle
EEDCDC cn:congruencereflexive
EEDFDG proposition:26B
EECFCG proposition:26B
EEDGDF lemma:congruencesymmetric
EEDGDE lemma:congruencetransitive
EQDD cn:equalityreflexive
COADD defn:collinear
NCADB lemma:NCorder
OSBADH defn:oppositeside
OSHADB lemma:oppositesidesymmetric
EQAA cn:equalityreflexive
COADA defn:collinear
RAACH lemma:ray4
OSCADB lemma:9.5
EEDADA cn:congruencereflexive
EQEA assumption
% Euclid fails to consider this possibility at all
EEDADE cn:equalitysub
RRCGD lemma:8.2
COCGA lemma:collinearorder
EQAG assumption
EQGA lemma:equalitysymmetric
RRCAD cn:equalitysub
RRDAC lemma:8.2
RRBAD cn:equalitysub
OSBADC lemma:oppositesidesymmetric
BEBAC lemma:rightcollinear
COBAC defn:collinear
COABC lemma:collinearorder
NEAG reductio
EEDGDA cn:equalitysub
RRSGD
COASC lemma:collinearorder
NEGA lemma:inequalitysymmetric
RRAGD lemma:collinearright
LTGDAD lemma:legsmallerhypotenuse
EEDEDG lemma:congruencesymmetric
EEDADG cn:equalitysub
EEADGD lemma:congruenceflip
LTGDGD lemma:lessthancongruence
NOLTGDGD lemma:trichotomy2
NEEA reductio
NEAE lemma:inequalitysymmetric
EQGA assumption
EEDADG cn:equalitysub
RRBED lemma:8.2
COBEA lemma:collinearorder
NEAE lemma:inequalitysymmetric
EEDADE cn:equalitysub
EEDEDA lemma:congruencesymmetric
RRQED
COAQB lemma:collinearorder
RRAED lemma:collinearright
LTEDAD lemma:legsmallerhypotenuse
EEDGDE
EEADED lemma:congruenceflip
LTEDED lemma:lessthancongruence
NOLTEDED lemma:trichotomy2
NEGA reductio
NEAG lemma:inequalitysymmetric
RRDGC
RRDEB
RRCGD lemma:8.2
RRBED lemma:8.2
COBEA lemma:collinearorder
RRAED lemma:collinearright
COCGA lemma:collinearorder
RRAGD lemma:collinearright
EAAEDAGD lemma:Euclid4
COAED assumption
COEAD lemma:collinearorder
COEAB lemma:collinearorder
COADB lemma:collinear4
NCADB
NCAED reductio
COAGD assumption
COGAC lemma:collinearorder
COGAD lemma:collinearorder
COACD lemma:collinear4
NCACD
NCAGD reductio
TRAED defn:triangle
TRAGD defn:triangle
RRAED
RRAGD
EEADAD cn:congruencereflexive
EEGDED lemma:congruenceflip
EEEDGD lemma:congruencesymmetric
EADAEDAG lemma:rightangleSSA
NCDAG lemma:NCorder
EADAGGAD lemma:ABCequalsCBA
EADAEGAD lemma:equalanglestransitive
EAGADDAE lemma:equalanglessymmetric
BECDJ
BEAJB
NCABC
ANBECKB+BEADK postulate:Pasch-outer
BECKB
BEADK
NOBEAEB assumption
NOBEAGC assumption
RABAE
ORBEBAE|EQEA|BEBEA lemma:ray1
BEBEA assumption
BEAEB axiom:betweennesssymmetry
NOBEBEA reductio
NEEA
cases BEBAE:BEBAE|EQEA|BEBEA
case 1:BEBAE
qedcase
case 2:EQEA
NOBEBAE assumption
NEEA
BEBAE reductio
qedcase
case 3:BEBEA
NOBEBAE assumption
BEAEB axiom:betweennesssymmetry
BEBAE reductio
qedcase
BEBAE cases
EEBABA cn:congruencereflexive
LTBABE defn:lessthan
EEBEBF lemma:congruencesymmetric
LTBABF lemma:lessthancongruence
RACAG
ORBECAG|EQGA|BECGA lemma:ray1
BECGA assumption
BEAGC axiom:betweennesssymmetry
NOBECGA reductio
NEGA
cases BECAG:BECAG|EQGA|BECGA
case 1:BECAG
qedcase
case 2:EQGA
NOBECAG assumption
NEGA
BECAG reductio
qedcase
case 3:BECGA
NOBECAG assumption
BEAGC axiom:betweennesssymmetry
BECAG reductio
qedcase
BECAG cases
EECACA cn:congruencereflexive
LTCACG defn:lessthan
EECGCF lemma:congruencesymmetric
LTCACF lemma:lessthancongruence
EECFFC cn:equalityreverse
LTCAFC lemma:lessthancongruence
EECAAC cn:equalityreverse
LTACFC lemma:lessthancongruence2
NCBAC lemma:NCorder
TRBAC defn:triangle
TGBAACBC proposition:20
ANBEBAL+EEALAC+LTBCBL defn:togethergreater
BEBAL
EEALAC
LTBCBL
EEACAL lemma:congruencesymmetric
LTALFC lemma:lessthancongruence2
LTBABF
BEBAL
RABCF
RACBF
BEBFC lemma:tworays
LTBLBC lemma:lessthanadditive2
LTBLBL lemma:lessthantransitive
NOLTBLBL lemma:trichotomy2
BEAGC reductio
BEBJA
COABE
OREQAB|EQAE|EQBE|BEBAE|BEABE|BEAEB defn:collinear
NEBE
NOBEAEB
NEEA
NEAB lemma:betweennotequal
BEABE assumption
RAABE lemma:ray4
RABAE
BEAEB lemma:tworays
BEBEB lemma:3.6a
NOBEBEB axiom:betweennessidentity
NOBEABE reductio
cases BEBAE:EQAB|EQAE|EQBE|BEBAE|BEABE|BEAEB
case 1:EQAB
NOBEBAE assumption
NEAB
BEBAE reductio
qedcase
case 2:EQAE
NOBEBAE assumption
NEAE
BEBAE reductio
qedcase
case 3:EQBE
NOBEBAE assumption
NEBE
BEBAE reductio
qedcase
case 4:BEBAE
qedcase
case 5:BEABE
NOBEBAE assumption
NOBEABE
BEBAE reductio
qedcase
case 6:BEAEB
NOBEBAE assumption
NOBEAEB
BEBAE reductio
qedcase
BEBAE cases
BEJAE lemma:3.6a
BEEAJ axiom:betweennesssymmetry
BECDJ
COCJE assumption
COJAE defn:collinear
COEJA lemma:collinearorder
COEJC lemma:collinearorder
NEJE lemma:betweennotequal
NEEJ lemma:inequalitysymmetric
COJAC lemma:collinear4
COCDJ defn:collinear
COJCD lemma:collinearorder
COJCA lemma:collinearorder
NECJ lemma:betweennotequal
NEJC lemma:inequalitysymmetric
COCDA lemma:collinear4
COACD lemma:collinearorder
NCACD
NCCJE reductio
ANBECMA+BEEMD postulate:Pasch-inner
BECMA
BEEMD
EQDD cn:equalityreflexive
NEAD lemma:NCdistinct
RAADD lemma:ray4
EQEE cn:equalityreflexive
RAAEE lemma:ray4
NCDAC lemma:NCorder
BEDME axiom:betweennesssymmetry
EADACDAC lemma:equalanglesreflexive
EQCC cn:equalityreflexive
RAACC lemma:ray4
BEAMC axiom:betweennesssymmetry
RAACM lemma:ray4
EADACDAM lemma:equalangleshelper
AODACDAE defn:anglelessthan
EAGADDAE
COGAD assumption
COAGC defn:collinear
COGAC lemma:collinearorder
COACD lemma:collinear4
NCGAD reductio
EAGADGAD lemma:equalanglesreflexive
RAAGC lemma:ray4
RAADD lemma:ray4
EAGADCAD lemma:equalangleshelper
NCCAD lemma:NCorder
EACADDAC lemma:ABCequalsCBA
EAGADDAC lemma:equalanglestransitive
EADACGAD lemma:equalanglessymmetric
EADACDAE lemma:equalanglestransitive
EADAEDAC lemma:equalanglessymmetric
AODAEDAE lemma:angleorderrespectscongruence2
NOAODAEDAE lemma:angletrichotomy
BEAEB reductio
RAAEB lemma:ray4
EQDD cn:equalityreflexive
NEAD lemma:NCdistinct
RAADD lemma:ray4
RAAEB lemma:ray4
COEAD assumption
COEAB lemma:collinearorder
COABD lemma:collinear4
NCEAD reductio
EAEADEAD lemma:equalanglesreflexive
EAEADBAD lemma:equalangleshelper
NEAG
% Now we have to prove BEAGC
% by switching (B,J,E) to (C,H,G) in the
% above argument
COACG
OREQAC|EQAG|EQCG|BECAG|BEACG|BEAGC defn:collinear
NECG
NOBEAGC assumption
NEGA
NEAC lemma:betweennotequal
BEACG assumption
RAACG lemma:ray4
RACAG
BEAGC lemma:tworays
BECGC lemma:3.6a
NOBECGC axiom:betweennessidentity
NOBEACG reductio
cases BECAG:EQAC|EQAG|EQCG|BECAG|BEACG|BEAGC
case 1:EQAC
NOBECAG assumption
NEAC
BECAG reductio
qedcase
case 2:EQAG
NOBECAG assumption
NEAG
BECAG reductio
qedcase
case 3:EQCG
NOBECAG assumption
NECG
BECAG reductio
qedcase
case 4:BECAG
qedcase
case 5:BEACG
NOBECAG assumption
NOBEACG
BECAG reductio
qedcase
case 6:BEAGC
NOBECAG assumption
NOBEAGC
BECAG reductio
qedcase
BECAG cases
BEHAG lemma:3.6a
BEGAH axiom:betweennesssymmetry
BEBDH
COBHG assumption
COHAG defn:collinear
COGHA lemma:collinearorder
COGHB lemma:collinearorder
NEHG lemma:betweennotequal
NEGH lemma:inequalitysymmetric
COHAB lemma:collinear4
COBDH defn:collinear
COHBD lemma:collinearorder
COHBA lemma:collinearorder
NEBH lemma:betweennotequal
NEHB lemma:inequalitysymmetric
COBDA lemma:collinear4
COABD lemma:collinearorder
NCABD
NCBHG reductio
ANBEBMA+BEGMD postulate:Pasch-inner
BEBMA
BEGMD
EQDD cn:equalityreflexive
NEAD lemma:NCdistinct
RAADD lemma:ray4
EQGG cn:equalityreflexive
RAAGG lemma:ray4
NCDAB lemma:NCorder
BEDMG axiom:betweennesssymmetry
EADABDAB lemma:equalanglesreflexive
EQBB cn:equalityreflexive
RAABB lemma:ray4
BEAMB axiom:betweennesssymmetry
RAABM lemma:ray4
EADABDAM lemma:equalangleshelper
AODABDAG defn:anglelessthan
EAGADDAE
EADAGEAD lemma:equalanglesflip
EAEADDAG lemma:equalanglessymmetric
COEAD assumption
COAEB defn:collinear
COEAB lemma:collinearorder
COABD lemma:collinear4
NCEAD reductio
COHAD assumption
COAHC defn:collinear
COHAC lemma:collinearorder
NEAH lemma:betweennotequal
NEHA lemma:inequalitysymmetric
COACD lemma:collinear4
NCHAD reductio
EAEADEAD lemma:equalanglesreflexive
NEAJ lemma:betweennotequal
RAAEB lemma:ray4
RAADD lemma:ray4
EAEADBAD lemma:equalangleshelper
NCBAD lemma:NCorder
EABADDAB lemma:ABCequalsCBA
EAEADDAB lemma:equalanglestransitive
EADABEAD lemma:equalanglessymmetric
EADABDAG lemma:equalanglestransitive
EADAGDAB lemma:equalanglessymmetric
AODAGDAG lemma:angleorderrespectscongruence2
NOAODAGDAG lemma:angletrichotomy
BEAGC reductio
RAAGC lemma:ray4
RAACG lemma:ray5
NCDAC lemma:NCorder
EADACDAC lemma:equalanglesreflexive
EADACDAG lemma:equalangleshelper
EAGADDAE
EADAGEAD lemma:equalanglesflip
EAEADDAG lemma:equalanglessymmetric
EABADEAD lemma:equalanglessymmetric
EABADDAG lemma:equalanglestransitive
EADAGDAC lemma:equalanglessymmetric
EABADDAC lemma:equalanglestransitive
BEBKC axiom:betweennesssymmetry
ANBECDJ+BEBDH+EABADDAC+BEADK+BEBKC
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