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SSCDAB
OSDABE
ANCOABG+COABH+BECGQ+BEDHQ+NCABC+NCABD defn:sameside
COABG
COABH
BECGQ
BEDHQ
NCABC
EQAB assumption
COABC defn:collinear
NEAB reductio
NEBA lemma:inequalitysymmetric
ANBEDWE+COABW+NCABD defn:oppositeside
BEDWE
NECG  lemma:betweennotequal
NEGC  lemma:inequalitysymmetric
NEGQ  lemma:betweennotequal
cases OSCABE:COCQD|NCCQD
 case 1:COCQD
  NOOSCABE assumption
   COQCD  lemma:collinearorder
   NEGH   assumption
    COABG
    COABH
    COCGQ defn:collinear
    CODHQ defn:collinear
    COQCG lemma:collinearorder
    NECQ  lemma:betweennotequal
    NEQC  lemma:inequalitysymmetric
    COCGD lemma:collinear4
    CODQH lemma:collinearorder
    CODQC lemma:collinearorder
    COCAB assumption
     COABC lemma:collinearorder
    NCCAB reductio
    ORNCCAB|NCDAB
    ANCOCAB+CODAB assumption
     ORNCCAB|NCDAB
    NOANCOCAB+CODAB reductio
    COGAB lemma:collinearorder
    COHAB lemma:collinearorder
    COGCD lemma:collinearorder
    COQDH lemma:collinearorder
    COQDC lemma:collinearorder
    NEDQ  lemma:betweennotequal
    NEQD lemma:inequalitysymmetric
    CODCH lemma:collinear4
    COHCD lemma:collinearorder
    EQCD assumption
     OSDABE
     OSCABE  cn:equalitysub
    NECD reductio
    NEAB
    EQGH  lemma:twolines2
   EQGH  reductio
   BEQGC axiom:betweennesssymmetry
   BEQHD axiom:betweennesssymmetry
   BEQGD cn:equalitysub
   NCEDG  assumption
    NCECG  assumption
     BEGCD  assumption
      OSDABE
      OSCABE  lemma:9.5b
     NOBEGCD reductio
     BEGDC  assumption
      COGCE assumption
       COECG lemma:collinearorder
      NCGCE reductio
      OSCABE  lemma:9.5a
     NOBEGDC reductio
     EQCD  lemma:outerconnectivity
     OSCABE cn:equalitysub
    COECG  reductio
    COQGD  defn:collinear
    COQGC  defn:collinear
    NEQG   lemma:betweennotequal
    COGDC  lemma:collinear4
    COCGD  lemma:collinearorder
    COCGE  lemma:collinearorder
    NEGC  lemma:betweennotequal
    NECG   lemma:inequalitysymmetric
    COGDE  lemma:collinear4
    COEDG  lemma:collinearorder
   COEDG  reductio
   COABW
   COABG
   CODWE  defn:collinear
   CODEW  lemma:collinearorder
   CODEG  lemma:collinearorder
   NEDE  lemma:betweennotequal
   COEWG  lemma:collinear4
   COEWD  lemma:collinearorder
   NEWE lemma:betweennotequal
   NEEW  lemma:inequalitysymmetric
   COWGD  lemma:collinear4 
   COBWG  lemma:collinear4
   COWGB   lemma:collinearorder
   COBAW  lemma:collinearorder
   COBAG  lemma:collinearorder
   COAWG  lemma:collinear4
   COWGA  lemma:collinearorder
   NEWG assumption
    COGDB  lemma:collinear4
    COGBD  lemma:collinearorder
    COGBA  lemma:collinearorder
    NEGB assumption
     COBDA lemma:collinear4
     COABD  lemma:collinearorder
     NCABD
    EQGB  reductio
    COGDA lemma:collinear4
    COGAD lemma:collinearorder
    COGAB lemma:collinearorder
    NEGA assumption
     COADB lemma:collinear4
     COABD lemma:collinearorder
     NCABD
    EQGA reductio
    EQAG lemma:equalitysymmetric
    EQBG lemma:equalitysymmetric
    EQAB  cn:equalitytransitive
    NEAB
   EQWG reductio
   BEDWE
   BEDGE  cn:equalitysub
   BEEGD  axiom:betweennesssymmetry
   BEGDC  assumption
    BEEGC  lemma:3.7b
    BECGE  axiom:betweennesssymmetry
    OSCABE  defn:oppositeside
   NOBEGDC reductio
   BEGCD  assumption
    BEEGC axiom:innertransitivity
    BECGE  axiom:betweennesssymmetry
    OSCABE defn:oppositeside
   NOBEGCD reductio
   BECGD assumption
    BEDGQ  cn:equalitysub
    BECGQ 
    BEDGC axiom:betweennesssymmetry
    BEGDC assumption
     BECDG  axiom:betweennesssymmetry
     BEDGC   
     BECGC  lemma:3.7a
     NECC  lemma:betweennotequal
     EQCC  cn:equalityreflexive
    NOBEGDC reductio
    BEGCD assumption
     BECGC axiom:innertransitivity
     NECC lemma:betweennotequal
     EQCC  cn:equalityreflexive
    NOBEGCD reductio
    BEQGD axiom:betweennesssymmetry
    BEQGC axiom:betweennesssymmetry
    EQCD  lemma:outerconnectivity
    OSCABE  cn:equalitysub
   NOBECGD reductio   
   COQCD  lemma:collinearorder
   COQGC  defn:collinear
   COQCG  lemma:collinearorder
   NEQC  lemma:betweennotequal
   COCDG  lemma:collinear4
   COGCD  lemma:collinearorder
   OREQGC|EQGD|EQCD|BECGD|BEGCD|BEGDC  defn:collinear
   cases OSCABE:EQGC|EQGD|EQCD|BECGD|BEGCD|BEGDC
    case 1:EQGC
     NOOSCABE  assumption
      COABG
      COABC  cn:equalitysub
      NCABC
     OSCABE reductio
    qedcase
    case 2:EQGD
     NOOSCABE assumption
      COABG
      COABD cn:equalitysub
      NCABD
     OSCABE reductio
    qedcase
    case 3:EQCD
     NOOSCABE assumption
      OSDABE 
      OSCABE cn:equalitysub
     OSCABE reductio
    qedcase
    case 4:BECGD
     NOOSCABE assumption
      NOBECGD
     OSCABE reductio
    qedcase
    case 5:BEGCD
     NOOSCABE assumption
      NOBEGCD
     OSCABE reductio
    qedcase
	case 6:BEGDC
     NOOSCABE assumption
      NOBEGDC
     OSCABE reductio
    qedcase
   OSCABE cases
  OSCABE reductio
 qedcase
 case 2:NCCQD
  NOOSCABE assumption
   COQCD  assumption
    COCQD  lemma:collinearorder
   NCQCD  reductio
   ANBECFH+BEDFG postulate:Pasch-inner
   BECFH
   BEDFG
   BEHFC  axiom:betweennesssymmetry
   BEGFD  axiom:betweennesssymmetry
   COEDG assumption
    NEWG assumption
     CODEG  lemma:collinearorder
     CODWE  defn:collinear
     COEDG  lemma:collinearorder
     COEDW  lemma:collinearorder
     NEDE   lemma:betweennotequal
     NEED lemma:inequalitysymmetric
     CODGW lemma:collinear4
     COGWD  lemma:collinearorder
     COABW
     COABG
     EQBB   cn:equalityreflexive
     COABB  defn:collinear
     NEGW   lemma:inequalitysymmetric
     COGWB lemma:collinear5
     COWDB  lemma:collinear4
     COBAW lemma:collinearorder
     COBAG lemma:collinearorder
     EQAA  cn:equalityreflexive
     COBAA defn:collinear
     NEGW
     COGWA lemma:collinear5
     COWDA lemma:collinear4
     NEDW  lemma:betweennotequal
     NEWD  lemma:inequalitysymmetric
     CODBA lemma:collinear4
     COABD lemma:collinearorder
     NCABD
    EQWG reductio
    BEDWE
    BEDGE  cn:equalitysub
    BEEGD  axiom:betweennesssymmetry
    BEGFD  axiom:betweennesssymmetry
    BEEGF  axiom:innertransitivity
    BEHFC
    COHCE assumption
     COHEC lemma:collinearorder
     COEHC lemma:collinearorder
     COCFH  defn:collinear
     COHCF  lemma:collinearorder
     COHCE lemma:collinearorder
     NECH  lemma:betweennotequal
     NEHC  lemma:inequalitysymmetric
     COCFE lemma:collinear4
     COEFC  lemma:collinearorder
     BEDFG
     BEDGE
     BEDFE  lemma:3.6b
     CODFE  defn:collinear
     COEFD lemma:collinearorder
     NEFE  lemma:betweennotequal
     NEEF  lemma:inequalitysymmetric
     COFCD lemma:collinear4
     COFDC  lemma:collinearorder
     CODFG  defn:collinear
     COFDG lemma:collinearorder
     NEDF  lemma:betweennotequal
     NEFD  lemma:inequalitysymmetric
     CODCG lemma:collinear4
     COGCD  lemma:collinearorder
     COCGQ  defn:collinear
     COGCQ lemma:collinearorder
     NECG  lemma:betweennotequal
     NEGC lemma:inequalitysymmetric
     COCDQ lemma:collinear4
     COQCD lemma:collinearorder
     NCQCD
    NCHCE reductio
    ANBEEMC+BEHGM postulate:Pasch-outer
    BEEMC
    BEHGM
    COHGM  defn:collinear
    COABH
    COABG
    COBHG lemma:collinear4
    COHGB lemma:collinearorder
    NEHG  lemma:betweennotequal
    COGMB lemma:collinear4
    COGBM  lemma:collinearorder
    COGBA  lemma:collinearorder
    cases COABM:EQBG|NEBG
     case 1:EQBG
      COBAH  lemma:collinearorder
      COBAG  lemma:collinearorder
      COAHG  lemma:collinear4
      COHGA   lemma:collinearorder
      COHGM   
      COGAM  lemma:collinear4
      COBAM   cn:equalitysub
      COABM   lemma:collinearorder
     qedcase
     case 2:NEBG
      NEGB  lemma:inequalitysymmetric
      COBMA  lemma:collinear4
      COABM  lemma:collinearorder
     qedcase
    COABM cases
    BECME  axiom:betweennesssymmetry
    ANBECME+COABM+NCABC
    OSCABE  defn:oppositeside
    NOOSCABE
   NCEDG  reductio
   OSFABE lemma:9.5b
   EQGH assumption
    CODHQ defn:collinear
    COCGQ defn:collinear
    COQHD lemma:collinearorder
    COQGC lemma:collinearorder
    COQHC cn:equalitysub
    NEHQ lemma:betweennotequal
    NEQH lemma:inequalitysymmetric
    COHDC lemma:collinear4
    COHDQ lemma:collinearorder
    NEDH lemma:betweennotequal
    NEHD lemma:inequalitysymmetric
    CODCQ lemma:collinear4
    COCQD lemma:collinearorder
    NCCQD 
   NEGH  reductio
   COHCE assumption
    BEEWD  axiom:betweennesssymmetry
    BEGFD  axiom:betweennesssymmetry
    ANBEEJF+BEGJW postulate:Pasch-inner
    BEEJF
    BEGJW
    COGJW  defn:collinear
    COEFJ  defn:collinear
    COFEJ  lemma:collinearorder
    COCFH  defn:collinear
    COCHF  lemma:collinearorder
    COCHE  lemma:collinearorder
    NECH   lemma:betweennotequal
    COHFE  lemma:collinear4
    COFEH  lemma:collinearorder
    BEEJF
    NEEF  lemma:betweennotequal
    NEFE  lemma:inequalitysymmetric
    COFEJ
    COFEH
    COGWJ  lemma:collinearorder
    COABG
    COABH
    COABW
    COGHW  lemma:collinear5
    COGWH lemma:collinearorder
    EQGW  assumption
     CODWE  defn:collinear
     CODGE  cn:equalitysub
     COEDG  lemma:collinearorder
     NCEDG
    NEGW  reductio
    COEJH lemma:collinear4
    COWJH lemma:collinear4
    COJHE lemma:collinearorder
    COJHW lemma:collinearorder
    EQHW assumption
     CODWE  defn:collinear
     CODHE  cn:equalitysub
     CODHQ  defn:collinear
     NEDH  lemma:betweennotequal
     COHEQ lemma:collinear4
     COHEC  lemma:collinearorder
     NEWE  lemma:betweennotequal
     NEHE   cn:equalitysub
     COEQC  lemma:collinear4
     COECQ lemma:collinearorder
     COECH lemma:collinearorder
     NEEC  assumption
      COCQH lemma:collinear4
      COHQC  lemma:collinearorder
      COHQD lemma:collinearorder
      NEHQ  lemma:betweennotequal
      COQCD lemma:collinear4
      NCQCD
     EQEC reductio
     COEWD lemma:collinearorder
     COCWD cn:equalitysub
     COCHD cn:equalitysub
     CODHC lemma:collinearorder
     CODHQ defn:collinear
     NEDH  lemma:betweennotequal
     COHCQ lemma:collinear4
     COHQC lemma:collinearorder
     COHQD lemma:collinearorder
     NEHQ  lemma:betweennotequal
     COQCD lemma:collinear4
     COCQD lemma:collinearorder
     NCCQD 
    NEHW reductio
    NEJH  assumption
     COHEW lemma:collinear4
     COHWE lemma:collinearorder
     COHWG lemma:collinearorder
     COWEG lemma:collinear4
     CODWE  defn:collinear
     COWED lemma:collinearorder
     NEWE  lemma:betweennotequal
     COEGD  lemma:collinear4
     COEDG  lemma:collinearorder
     NCEDG
    EQJH reductio
    BEEJF
    BEEHF  cn:equalitysub
    BEFHE  axiom:betweennesssymmetry
    BECFH
    BECHE  lemma:3.7a
    COABH
    OSCABE  defn:oppositeside
    NOOSCABE
   NCHCE reductio
   OSCABE lemma:9.5a
   NOOSCABE
  OSCABE reductio
 qedcase
OSCABE cases