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EEABab
EEACac
EABACbac
NCbac  lemma:equalanglesNC
ANRAABU+RAACV+RAabu+RAacv+EEAUau+EEAVav+EEUVuv+NCBAC defn:equalangles
RAABU
RAabu
RAacv
EEAVav
EEUVuv
NCBAC
NEab  lemma:ray2
NEba  lemma:inequalitysymmetric
COABC  assumption
 COBAC lemma:collinearorder
NCABC reductio 
EQAB   assumption
 COABC  defn:collinear
 COBAC  lemma:collinearorder
NEAB   reductio
EQAC  assumption
 COABC  defn:collinear
 COBAC  lemma:collinearorder
NEAC   reductio
NECA   lemma:inequalitysymmetric
EQac  assumption
 CObac defn:collinear
NEac   reductio
NEca   lemma:inequalitysymmetric
EQbc  assumption
 CObac defn:collinear
NEbc  reductio
NEcb   lemma:inequalitysymmetric
EQBC   assumption 
 COABC  defn:collinear
 COBAC lemma:collinearorder
NEBC  reductio
NECB   lemma:inequalitysymmetric
ORBEAUB|EQBU|BEABU  lemma:ray1
cases EEBVbv:BEAUB|EQBU|BEABU
 case 1:BEAUB
  EEAUau
  EEABab
  EEAUAU cn:congruencereflexive
  LTAUAB  defn:lessthan
  LTAUab  lemma:lessthancongruence
  ANBEawb+EEawAU  defn:lessthan
  BEawb
  EEawAU
  EEawau  lemma:congruencetransitive
  NEab    lemma:betweennotequal
  RAabw   lemma:ray4
  EEawau  lemma:congruencetransitive
  EQwu    lemma:layoffunique
  BEaub   cn:equalitysub
  EEUBub  lemma:differenceofparts
  EEUVuv
  EEAVav
  EEAUau
  EEVBvb  axiom:5-line
  EEBVbv  lemma:congruenceflip
 qedcase
 case 2:EQBU
  EEUVuv
  EEBVuv  cn:equalitysub
  EEabAB  lemma:congruencesymmetric
  EEABAB  cn:congruencereflexive
  EEABAU  cn:equalitysub
  EEAUau  
  EEabAU  lemma:congruencetransitive
  EEabau  lemma:congruencetransitive
  ORBEaub|EQbu|BEabu  lemma:ray1
  cases EQbu:BEaub|EQbu|BEabu 
   case 1: BEaub
    NEbu  assumption
     NOEEauab lemma:partnotequalwhole
     EEauab  lemma:congruencesymmetric
    EQbu reductio
   qedcase
   case 2: EQbu
   qedcase
   case 3: BEabu
    NEbu assumption
    NOEEabau lemma:partnotequalwhole
    EEabAB  lemma:congruencesymmetric
    EEABAB  cn:congruencereflexive
    EEABAU  cn:equalitysub
    EEAUau
    EEABau  lemma:congruencetransitive
    EEabau  lemma:congruencetransitive
    EQbu  reductio
   qedcase
  EQbu  cases
  EEUVuv
  EEBVbv  cn:equalitysub
 qedcase
 case 3: BEABU
  EEAUau
  EEABAB cn:congruencereflexive
  LTABAU  defn:lessthan
  LTABau  lemma:lessthancongruence
  ANBEafu+EEafAB  defn:lessthan
  BEafu
  NEau   lemma:betweennotequal
  RAauf  lemma:ray4
  RAabu
  RAaub   lemma:ray5
  RAabf   lemma:ray3
  EEafAB
  EEABab
  EEafab  lemma:congruencetransitive
  EQfb   lemma:layoffunique
  BEabu   cn:equalitysub  
  EEBUbu lemma:differenceofparts
  BEabu   lemma:betweennesspreserved 
  EEABab
  EEBUbu   lemma:differenceofparts
  EEAVav
  EEUVuv
  EEBVbv  lemma:interior5
 qedcase
EEBVbv  cases
RAACV
ORBEAVC|EQCV|BEACV lemma:ray1
cases EEBCbc:BEAVC|EQCV|BEACV
 case 1: BEAVC
  EEAVav
  EEAVAV cn:congruencereflexive
  LTAVAC  defn:lessthan   
  LTAVac lemma:lessthancongruence
  ANBEagc+EEagAV defn:lessthan
  BEagc
  NEag   lemma:betweennotequal
  RAagc  lemma:ray4
  RAacg  lemma:ray5
  RAacv   
  EEagAV
  EEagav lemma:congruencetransitive
  EQgv   lemma:layoffunique 
  BEavc  cn:equalitysub
  EEVCvc  lemma:differenceofparts
  EEABab
  EEAVav
  EEVCvc
  EEVBvb  lemma:congruenceflip
  EEBCbc   axiom:5-line
 qedcase
 case 2: EQCV
  EEAVav
  EEACav  cn:equalitysub
  EEACac
  EEacAC lemma:congruencesymmetric
  EEacav lemma:congruencetransitive
  RAacv
  NEac   lemma:ray2
  EQcc   cn:equalityreflexive
  RAacc  lemma:ray4
  EQcv  lemma:layoffunique
  EEBCbv  cn:equalitysub
  EEBCbc  cn:equalitysub
 qedcase
 case 3: BEACV
  EEAVav
  EEACAC cn:congruencereflexive
  LTACAV  defn:lessthan   
  LTACav lemma:lessthancongruence
  ANBEagv+EEagAC defn:lessthan
  BEagv
  EEagAC
  NEag   lemma:betweennotequal
  RAagv  lemma:ray4
  RAavg  lemma:ray5
  EEagac lemma:congruencetransitive
  EEacag lemma:congruencesymmetric
  RAavc   lemma:ray5
  EQcg   lemma:layoffunique 
  BEacv  cn:equalitysub
  EECVcv  lemma:differenceofparts
  EEABab
  EEVBvb  lemma:congruenceflip
  EECBcb   lemma:interior5
  EEBCbc   lemma:congruenceflip
 qedcase
EEBCbc  cases
EQAA   cn:equalityreflexive
EQCC   cn:equalityreflexive
EQaa   cn:equalityreflexive
EQcc   cn:equalityreflexive
EQBB   cn:equalityreflexive
EQbb   cn:equalityreflexive
NEBA   lemma:inequalitysymmetric
RABAA  lemma:ray4
RABCC  lemma:ray4
RAbaa   lemma:ray4
RAbcc  lemma:ray4
EEBAba  lemma:congruenceflip
EEBCbc
EEACac
NCABC
EAABCabc   defn:equalangles
RACAA  lemma:ray4
RACBB  lemma:ray4
RAcaa   lemma:ray4
RAcbb  lemma:ray4
EECAca  lemma:congruenceflip
EECBcb  lemma:congruenceflip
EEABab
COACB   assumption
 COABC   lemma:collinearorder
 NCABC
NCACB   reductio
EAACBacb   defn:equalangles
ANEEBCbc+EAABCabc+EAACBacb