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TGAaBbCc
TGAaCcBb
TGBbCcAa
NEFE
ANBEAaP+EEaPBb+LTCcAP  defn:togethergreater
BEAaP
EEaPBb
LTCcAP
NEAa   lemma:betweennotequal
NEaP   lemma:betweennotequal
NEBb   axiom:nocollapse
NECc   lemma:lessthannotequal
ANRAFEG+EEFGBb  lemma:layoff
RAFEG
EEFGBb
EEBbFG   lemma:congruencesymmetric
NEFG     axiom:nocollapse
NEGF     lemma:inequalitysymmetric
ANBEFGH+EEGHCc  lemma:extension
BEFGH
ANBEGFD+EEFDAa  lemma:extension
BEGFD
EEFDAa
EEDFAa   lemma:congruenceflip
BEDFG    axiom:betweennesssymmetry 
NEFD    lemma:betweennotequal
NEGH   lemma:betweennotequal    
CILFFD     postulate:Euclid3
CIRGGH     postulate:Euclid3
EEGHGH    cn:congruencereflexive
ONHR     defn:on
EEFGBb
EEGHCc
EEDFAa
TGBbCcAa
LTDFFH    lemma:together
ANBEFMH+EEFMDF  defn:lessthan
BEFMH
EEFMDF
EEDFAa
EEFMAa   lemma:congruencetransitive
EEAaFM   lemma:congruencesymmetric
EEAaFD  lemma:congruencesymmetric
EEFMFD   cn:congruencetransitive
OCHL     defn:outside
TGAaBbCc 
EEDFAa
EEFGBb
BEDFG
EECcCc   cn:congruencereflexive
LTCcDG  lemma:together
EEDGGD   cn:equalityreverse
LTCcGD  lemma:lessthancongruence
ANBEGND+EEGNCc  defn:lessthan
BEGND
BEDFG
BEFGH
BEDFH  lemma:3.7b
BEFMH
BEDFM  axiom:innertransitivity
EEFDAa  lemma:congruenceflip
BEDNG   axiom:betweennesssymmetry
NEFM   lemma:betweennotequal
ANBEFMJ+EEMJCc  lemma:extension
BEFMJ
BEDFM
BEDFJ   lemma:3.7b
EEFGBb
EEFMAa
EEMJCc
TGAaCcBb
ANLTFGFJ+NEAa+NECc+NEBb lemma:together
LTFGFJ
ANBEFQJ+EEFQFG  defn:lessthan
BEFQJ
EEFQFG
NEFJ  lemma:betweennotequal
RAFJQ lemma:ray4
BEDFG
BEDFJ
RAFGJ defn:ray
RAFJG  lemma:ray5
EQQG    lemma:layoffunique
EQGQ   lemma:equalitysymmetric
BEFGJ   cn:equalitysub
BEDFG
BEDGJ   lemma:3.7a
EEGNCc
EEMJCc
EECcMJ  lemma:congruencesymmetric
EEGNMJ  lemma:congruencetransitive
EENGMJ  lemma:congruenceflip
BEDMJ   lemma:3.7a
BEDNG   
BEDNM   lemma:subtractequals
EEFMAa
EEGNCc
BEDFM
EEFDFD cn:congruencereflexive
ICNL   lemma:ondiameter
EECcGH  lemma:congruencesymmetric
EECcGN  lemma:congruencesymmetric
EEGNGH cn:congruencetransitive
ONNR  defn:on
ONHR
OCHL
ANONKL+ONKR  postulate:circle-circle
ONKL
ONKR
EEFKFD   axiom:circle-center-radius
EEFKAa   lemma:congruencetransitive
EEGKGH   axiom:circle-center-radius
EEGKCc   lemma:congruencetransitive
COFGK    assumption
 OREQFG|EQFK|EQGK|BEGFK|BEFGK|BEFKG  defn:collinear
 cases NCFGK:EQFG|EQFK|EQGK|BEGFK|BEFGK|BEFKG
  case 1:EQFG
   COFGK assumption
    NEFG
   NCFGK  reductio
  qedcase
  case 2: EQFK
   EEFKAa
   NEAa
   EEAaFK  lemma:congruencesymmetric
   COFGK assumption
    NEFK    axiom:nocollapse 
   NCFGK  reductio
  qedcase
  case 3:EQGK
   EEGKCc
   EECcGK  lemma:congruencesymmetric
   COFGK assumption
    NECc
    NEGK  axiom:nocollapse
   NCFGK  reductio
  qedcase
  case 4: BEGFK
   BEKFG  axiom:betweennesssymmetry
   EEFKAa
   EEKFAa lemma:congruenceflip
   EEGKCc
   TGAaBbCc
   ANBEAaS+EEaSBb+LTCcAS  defn:togethergreater
   EEaSBb
   LTCcAS
   EEAaKF   lemma:congruencesymmetric
   EEaSFG   lemma:congruencetransitive
   BEAaS
   BEKFG
   EEASKG   cn:sumofparts
   EEASGK   lemma:congruenceflip
   LTCcGK   lemma:lessthancongruence
   EECcGK   lemma:congruencesymmetric
   LTGKGK   lemma:lessthancongruence2
   COFGK assumption
    NOLTGKGK  lemma:trichotomy2
   NCFGK   reductio
  qedcase
  case 5: BEFGK
   EEFKAa
   EEGKCc
   EEFGBb
   TGBbCcAa
   ANBEBbS+EEbSCc+LTAaBS defn:togethergreater
   BEBbS
   EEbSCc
   LTAaBS
   EECcbS  lemma:congruencesymmetric
   EEGKbS  lemma:congruencetransitive
   EEFKBS  cn:sumofparts
   EEAaFK  lemma:congruencesymmetric
   LTFKBS  lemma:lessthancongruence2
   EEBSFK  lemma:congruencesymmetric
   LTFKFK  lemma:lessthancongruence
   COFGK  assumption
    NOLTFKFK  lemma:trichotomy2
   NCFGK  reductio
  qedcase
  case 6:BEFKG
   EEFKAa
   EEGKCc
   TGAaCcBb   
   ANBEAaS+EEaSCc+LTBbAS  defn:togethergreater
   BEAaS
   EEaSCc
   LTBbAS
   LTFGAS   lemma:lessthancongruence2
   EECcaS   lemma:congruencesymmetric
   EEGKaS   lemma:congruencetransitive
   EEKGaS   lemma:congruenceflip
   EEFGAS   cn:sumofparts
   EEASFG   lemma:congruencesymmetric
   LTFGFG   lemma:lessthancongruence
   COFGK  assumption
    NOLTFGFG  lemma:trichotomy2
   NCFGK  reductio
  qedcase
 NCFGK cases
NCFGK    reductio
TRFGK    defn:triangle
ANEEFGBb+EEFKAa+EEGKCc+RAFEG+TRFGK