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RRABD
COABC
NECB
OREQAB|EQAC|EQBC|BEBAC|BEABC|BEACB  defn:collinear
NCABD  lemma:rightangleNC
EQAB   assumption
 NCAAD  cn:equalitysub
 EQAA  cn:equalityreflexive
 CODAA defn:collinear
 COAAD lemma:collinearorder
NEAB  reductio
RRDBA   lemma:8.2
cases RRDBC:EQAB|EQAC|EQBC|BEBAC|BEABC|BEACB
 case 1:EQAB
  NORRDBC assumption
   COABD  defn:collinear
  RRDBC reductio
 qedcase
 case 2:EQAC
  RRDBC  cn:equalitysub
 qedcase
 case 3:EQBC
  NORRDBC assumption
  EQCB  lemma:equalitysymmetric
  NECB
  RRDBC reductio
 qedcase
 case 4:BEBAC
  NEBA   lemma:inequalitysymmetric
  RABAC   lemma:ray4
  RRDBC   lemma:8.3
 qedcase
 case 5:BEABC
  ANBEABE+EEABEB+EEADED+NEBD  defn:rightangle
  EEABEB
  EEADED
  BEABE
  NEBD
  BEEBA  axiom:betweennesssymmetry
  EEEBAB lemma:congruencesymmetric
  EEEDAD lemma:congruencesymmetric
  ANBEEBA+EEEBAB+EEADED+NEBD
  RREBD  defn:rightangle
  RRDBE  lemma:8.2
  BEABE  axiom:betweennesssymmetry
  ANBEABC+BEABE
  RABEC  defn:ray
  RRDBC  lemma:8.3  
 qedcase
 case 6:BEACB
  BEBCA  axiom:betweennesssymmetry
  NECB  lemma:betweennotequal
  NEBC  lemma:inequalitysymmetric
  RABCA  lemma:ray4
  RRDBA  lemma:8.2 
  RABAC   lemma:ray5
  RRDBC   lemma:8.3
 qedcase
RRDBC cases
RRCBD lemma:8.2