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RRBAC
RRAMp
COBCp
COBCM
NCBAC  lemma:rightangleNC
NECB  lemma:NCdistinct
EQBM assumption
 RRABp  cn:equalitysub
 COpBC  lemma:collinearorder
 RRpBA  lemma:8.2
 RRCBA  lemma:collinearright
 NORRCBA lemma:8.7
NEBM reductio
RRpMA  lemma:8.2
COCBp  lemma:collinearorder
COCBM  lemma:collinearorder
NCBAC  lemma:rightangleNC
NECB  lemma:NCdistinct
COBpM lemma:collinear4
COpMB  lemma:collinearorder
RRBMA  lemma:collinearright
COBCp  lemma:collinearorder
COBCM  lemma:collinearorder
NEBC lemma:inequalitysymmetric
COCpM  lemma:collinear4
COpMC  lemma:collinearorder
RRCAB  lemma:8.2
EQCM assumption
 RRACp cn:equalitysub
 COpCB lemma:collinearorder
 RRpCA  lemma:8.2
 RRBCA  lemma:collinearright
 NORRBCA  lemma:8.7
NECM  reductio
RRCMA  lemma:collinearright
RRAMB  lemma:8.2
RRAMC  lemma:8.2
LTMBAB   lemma:legsmallerhypotenuse
LTBABC   lemma:legsmallerhypotenuse
EEBAAB  cn:equalityreverse
LTABBC  lemma:lessthancongruence2
LTMBBC   lemma:lessthantransitive
EEMBBM   cn:equalityreverse
LTBMBC   lemma:lessthancongruence2
LTMCAC  lemma:legsmallerhypotenuse
EEMCCM  cn:equalityreverse
LTCMAC  lemma:lessthancongruence2
LTACBC  lemma:legsmallerhypotenuse
LTCMBC  lemma:lessthantransitive
BEMBC   assumption
 BECBM  axiom:betweennesssymmetry
 EECBCB  cn:congruencereflexive
 LTCBCM  defn:lessthan
 EECBBC  cn:equalityreverse
 LTBCCM  lemma:lessthancongruence2
 NOLTCMBC lemma:trichotomy2
NOBEMBC reductio
COBCM
OREQBC|EQBM|EQCM|BECBM|BEBCM|BEBMC defn:collinear
cases RABCM:EQBC|EQBM|EQCM|BECBM|BEBCM|BEBMC
 case 1:EQBC
  NORABCM assumption
   NEBC
  RABCM reductio
 qedcase
 case 2:EQBM
  NORABCM assumption
   NEBM
  RABCM reductio
 qedcase
 case 3:EQCM
  NORABCM assumption
   NECM
  RABCM reductio
 qedcase
 case 4:BECBM
  NORABCM assumption
   BEMBC axiom:betweennesssymmetry
   NOBEMBC
  RABCM reductio
 qedcase
 case 5:BEBCM
  RABCM  lemma:ray4
 qedcase
 case 6:BEBMC
  RABMC  lemma:ray4
  RABCM  lemma:ray5
 qedcase
RABCM cases
BEBCM assumption
 EEBCBC  cn:congruencereflexive
 LTBCBM  defn:lessthan
 NOLTBMBC lemma:trichotomy2
NOBEBCM reductio
cases RACBM:EQBC|EQBM|EQCM|BECBM|BEBCM|BEBMC
 case 1:EQBC
  NORACBM assumption
   NEBC
  RACBM reductio
 qedcase
 case 2:EQBM
  NORACBM assumption
   NEBM
  RACBM reductio
 qedcase
 case 3:EQCM
  NORACBM assumption
   NECM
  RACBM reductio
 qedcase
 case 4:BECBM
  RACBM  lemma:ray4
 qedcase
 case 5:BEBCM
  NORACBM assumption
   NOBEBCM
  RACBM reductio
 qedcase
 case 6:BEBMC
  BECMB axiom:betweennesssymmetry
  RACMB lemma:ray4
  RACBM  lemma:ray5
 qedcase
RACBM cases
BEBMC  lemma:tworays