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OSPABC
RARQP
COABR
ORBERPQ|EQQP|BERQP  lemma:ray1
cases OSQABC:NCCPR|COCPR
 case 1:NCCPR
  cases OSQABC:BERPQ|EQQP|BERQP
   case 1:BERPQ
    CORQC assumption
     COQRC lemma:collinearorder
     CORQP lemma:rayimpliescollinear
     COQRP  lemma:collinearorder
     NERQ  lemma:betweennotequal
     NEQR  lemma:inequalitysymmetric
     CORCP lemma:collinear4
     COCPR lemma:collinearorder
     NCCPR  
    NCRQC reductio
    OSQABC  lemma:9.5a
   qedcase
   case 2:EQQP
    OSQABC  cn:equalitysub
   qedcase
   case 3:BERQP
    OSQABC  lemma:9.5b
   qedcase
  OSQABC cases
 qedcase
 case 2:COCPR
  ANBEPLC+COABL+NCABP  defn:oppositeside
  BEPLC
  COABL
  NCABP
  COPCL  defn:collinear
  COCPL  lemma:collinearorder
  NEPC  lemma:betweennotequal
  NECP  lemma:inequalitysymmetric
  COPLR  lemma:collinear4
  EQAB assumption
   COABP defn:collinear
  NEAB reductio
  COBLR lemma:collinear4
  COLRP lemma:collinearorder
  COLRB lemma:collinearorder
  NELR assumption
   CORPB lemma:collinear4
   CORBP lemma:collinearorder
   CORBA lemma:collinearorder
   NERB assumption
    COBPA lemma:collinear4
    COABP lemma:collinearorder
    NCABP
   EQRB  reductio
   NEBA  lemma:inequalitysymmetric
   NERA  cn:equalitysub
   COBAR lemma:collinearorder
   COBAL  lemma:collinearorder
   COALR  lemma:collinear4
   COLRA  lemma:collinearorder
   CORPA  lemma:collinear4
   CORAP  lemma:collinearorder
   CORAB lemma:collinearorder
   COAPB  lemma:collinear4
   COABP  lemma:collinearorder
   NCABP
  EQLR  reductio
  BEPRC  cn:equalitysub 
  BECRP  axiom:betweennesssymmetry
  cases BECRQ:BERPQ|EQQP|BERQP 
   case 1:BERPQ
    BECRQ  lemma:3.7b
   qedcase
   case 2:EQQP
    BECRQ  cn:equalitysub
   qedcase
   case 3: BERQP
    BECRQ  axiom:innertransitivity
   qedcase
  BECRQ cases
  BEQRC axiom:betweennesssymmetry
  COABQ assumption
   COABR 
   COBQR  lemma:collinear4
   CORQP lemma:rayimpliescollinear
   COQRB  lemma:collinearorder
   COQRP  lemma:collinearorder
   NEQR  lemma:betweennotequal
   CORBP lemma:collinear4
   CORBA lemma:collinearorder
   NERB assumption
    COBPA lemma:collinear4
    COABP lemma:collinearorder
    NCABP
   EQRB reductio
   NEBA lemma:inequalitysymmetric
   NERA  cn:equalitysub
   COBAR lemma:collinearorder
   COBAQ lemma:collinearorder
   NEBA lemma:inequalitysymmetric
   COAQR lemma:collinear4
   COQRA lemma:collinearorder
   COQRP
   CORAP lemma:collinear4
   CORAB lemma:collinearorder
   COAPB lemma:collinear4
   COABP lemma:collinearorder
   NCABP
  NCABQ reductio
  ANBEQRC+COABR+NCABQ
  OSQABC defn:oppositeside
 qedcase
OSQABC cases