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SSEFAC
COABC
RABFG
ANCOACU+COACV+BEEUQ+BEFVQ+NCACE+NCACF defn:sameside
COACU
COACV
BEEUQ
BEFVQ
NCACE
NCACF 
OSFACQ   defn:oppositeside
COACB   lemma:collinearorder
EQAC assumption
 COACF defn:collinear
 NCACF
NEAC reductio
COBFG  lemma:rayimpliescollinear
COBGF  lemma:collinearorder
COACB  lemma:collinearorder
NOOSGACQ  assumption
 EQFG assumption
  OSGACQ cn:equalitysub 
 NEFG reductio 
 EQBV assumption
  BEFBQ  cn:equalitysub
  ORBEBGF|EQFG|BEBFG  lemma:ray1
  cases BEGBQ:BEBGF|EQFG|BEBFG
   case 1:BEBGF
    BEFGB axiom:betweennesssymmetry
    BEGBQ  lemma:3.6a
   qedcase
   case 2:EQFG
    NOBEGBQ assumption
     NEFG
    BEGBQ reductio
   qedcase
   case 3:BEBFG
	BEGFB axiom:betweennesssymmetry
    BEGBQ lemma:3.7a
   qedcase
  BEGBQ cases
  COACG  assumption
   COACB  lemma:collinearorder
   COCGB  lemma:collinear4
   COGBC  lemma:collinearorder
   COGBF  lemma:collinearorder
   NEBG  lemma:raystrict
   NEGB  lemma:inequalitysymmetric
   COBCF lemma:collinear4
   NEBC assumption
	COBCA lemma:collinearorder
    COCFA lemma:collinear4
    COACF  lemma:collinearorder
   EQBC reductio
   COABG cn:equalitysub
   COGBA  lemma:collinearorder
   COGBF 
   COBAF  lemma:collinear4
   COABF lemma:collinearorder
   COACF  cn:equalitysub
   NCACF  
  NCACG  reductio
  OSGACQ defn:oppositeside
 NEBV reductio
 COQFB  assumption
  COFVQ  defn:collinear
  COQFV  lemma:collinearorder
  NEFQ  lemma:betweennotequal
  NEQF  lemma:inequalitysymmetric
  COFBV  lemma:collinear4
  NEAC
  COCBV  lemma:collinear4
  COBVF  lemma:collinearorder
  COBVC  lemma:collinearorder
  COVFC  lemma:collinear4
  COVCF lemma:collinearorder
  COVCA  lemma:collinearorder
  NEVC  assumption
   COCFA  lemma:collinear4
   COACF  lemma:collinearorder
   NCACF
  EQVC  reductio
  NEAC
  NEAV  cn:equalitysub
  NEVA  lemma:inequalitysymmetric
  COCAB lemma:collinearorder
  COCAV lemma:collinearorder
  NECA  lemma:inequalitysymmetric
  COABV  lemma:collinear4
  COBVA  lemma:collinearorder
  COVFA  lemma:collinear4
  COVAF  lemma:collinearorder
  COVAC lemma:collinearorder
  COAFC  lemma:collinear4
  COACF  lemma:collinearorder
  NCACF
 NCQFB reductio
 ORBEBGF|EQFG|BEBFG  lemma:ray1
  cases OSGACQ:BEBGF|EQFG|BEBFG
   case 1:BEBGF 
    OSGACQ lemma:9.5b
   qedcase
   case 2:EQFG
    OSGACQ  cn:equalitysub
   qedcase
   case 3:BEBFG
    COBGQ  assumption
     COGBF  lemma:collinearorder
     NEBG lemma:betweennotequal
     NEGB  lemma:inequalitysymmetric
     COGBQ  lemma:collinearorder
     COBFQ  lemma:collinear4
     COQFB  lemma:collinearorder
     NCQFB
    NCBGQ  reductio
    OSGACQ   lemma:9.5a
   qedcase
  OSGACQ cases
 OSGACQ reductio
ANBEGHQ+COACH+NCACG defn:oppositeside
NCACG
BEGHQ
COACH 
SSEGAC   defn:sameside