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TPABcd
BECcd
NECc  lemma:betweennotequal
NEcd  lemma:betweennotequal
NECd   lemma:betweennotequal
ANNEAB+NEcd+NOMEABcd+SScdAB  defn:tarski_parallel
NEAB
NEcd
SScdAB
ANCOABp+COABr+BEcpq+BEdrq+NCABc+NCABd  defn:sameside
COABp
COABr
BEcpq
BEdrq
NCABc
NCABd
BEqrd axiom:betweennesssymmetry
COCcd  defn:collinear
COcdC  lemma:collinearorder
BEdcC  axiom:betweennesssymmetry
BEqrd
BEqpc axiom:betweennesssymmetry
EQpr assumption
 COqrd  defn:collinear
 COqpc   defn:collinear
 COqpd cn:equalitysub
 NEqp lemma:betweennotequal
 COpcd lemma:collinear4
 COcdp  lemma:collinearorder
 MEABcd defn:meet
 NOMEABcd
NEpr reductio
COqpc defn:collinear
COqdC  assumption
 COdcC defn:collinear
 COCdc lemma:collinearorder
 COCdq lemma:collinearorder
 NECd  lemma:betweennotequal
 COdcq lemma:collinear4
 COcqd lemma:collinearorder
 COcqp lemma:collinearorder
 NEqc  lemma:betweennotequal
 NEcq  lemma:inequalitysymmetric
 COqdp  lemma:collinear4
 COqrd defn:collinear
 COqdr lemma:collinearorder
 NEqd lemma:betweennotequal
 COdpr lemma:collinear4
 COABp
 COABr
 COBpr  lemma:collinear4
 COBAp lemma:collinearorder
 COBpA lemma:collinearorder
 COBAr lemma:collinearorder
 NEBA  lemma:inequalitysymmetric
 COApr lemma:collinear4
 NEBp assumption
  COprA  lemma:collinear4
  COprd  lemma:collinearorder
  COrAd  lemma:collinear4
  COrAB  lemma:collinearorder
  NErA assumption
   COAdB lemma:collinear4
   COABd  lemma:collinearorder
   NCABd
  EQrA  reductio
  COpAd cn:equalitysub
  COpAB  lemma:collinearorder
  NEpA assumption
   COAdB lemma:collinear4
   COABd  lemma:collinearorder
  EQpA  reductio
  EQrp  cn:equalitytransitive
  COqpc
  COqrd
  COqpd  cn:equalitysub
  NEqp  lemma:betweennotequal
  COpcd  lemma:collinear4
  COcdp  lemma:collinearorder
  MEABcd  defn:meet
  NOMEABcd
 EQBp reductio
 COrAB lemma:collinearorder
 COdBr  cn:equalitysub
 COrBd  lemma:collinearorder
 COrBA  lemma:collinearorder
 NErB assumption
  COBdA lemma:collinear4
  COABd lemma:collinearorder
 EQrB reductio
 EQpB lemma:equalitysymmetric
 EQpr cn:equalitytransitive
 NEpr 
NCqdC reductio
ANBEqEc+BECEr  postulate:Pasch-inner
BEqEc
COqEc defn:collinear
COqcp  lemma:collinearorder
COqcE  lemma:collinearorder
NEqc  lemma:betweennotequal
COcpE  lemma:collinear4
NErp  lemma:inequalitysymmetric
ANBErpJ+EEpJrp lemma:extension
BErpJ
BEJpr  axiom:betweennesssymmetry
COJpr  defn:collinear
NEJr   lemma:betweennotequal
NEpr   lemma:betweennotequal
NEJp   lemma:betweennotequal
BECEr
COABp
COABr
COBpr  lemma:collinear4
COBAp  lemma:collinearorder
COBAr  lemma:collinearorder
NEBA  lemma:inequalitysymmetric
COApr  lemma:collinear4
COprA  lemma:collinearorder
COprB  lemma:collinearorder
MECdJr  assumption
 ANNECd+NEJr+COCdK+COJrK  defn:meet
 NECd
 NEJr
 COCdK
 COJrK
 COCcd  defn:collinear
 COCdc  lemma:collinearorder
 NEcd lemma:betweennotequal
 NEdc lemma:inequalitysymmetric
 COdcK  lemma:collinear4
 COcdK  lemma:collinearorder
 COrJp  lemma:collinearorder
 NErJ  lemma:betweennotequal
 COrJK  lemma:collinearorder
 COJpK  lemma:collinear4
 COJpr  lemma:collinearorder
 NEpJ lemma:betweennotequal
 NEJp  lemma:inequalitysymmetric
 COpKr  lemma:collinear4
 COprK  lemma:collinearorder
 COprA
 COprB 
 COABK  lemma:collinear5
 MEABcd  defn:meet
 NOMEABcd
NOMECdJr reductio
BEcEp  lemma:collinearbetween
BEpEc  axiom:betweennesssymmetry
BEqpE  axiom:innertransitivity
NEpr
NCprc  lemma:NChelper
NCpcr  lemma:NCorder
COqpc  defn:collinear
COpcq  lemma:collinearorder
EQcc   cn:equalityreflexive
COpcc  defn:collinear
NEqc   lemma:betweennotequal
NCqcr  lemma:NChelper
NCqrc  lemma:NCorder
NEqd  lemma:betweennotequal
EQqq  cn:equalityreflexive
COdcC  lemma:collinearorder
NECd  lemma:betweennotequal
NEdC  lemma:inequalitysymmetric
NCdqC  lemma:NCorder
COqrd defn:collinear
COdqr lemma:collinearorder
COdqq  defn:collinear
EQrC  assumption
 COcdC
 COABr
 COABC  cn:equalitysub
 MEABcd  defn:meet
 NOMEABcd
NErC reductio
EQrq assumption
 COrqc defn:collinear
 COqrc lemma:collinearorder
NErq reductio
NCrqC  lemma:NChelper
NCrCq   lemma:NCorder
BErEC  axiom:betweennesssymmetry
BEqpE
ANBEqFC+BErpF  postulate:Pasch-outer
BEqFC
BECFq  axiom:betweennesssymmetry
BErpF
COrpF  defn:collinear
COrpA  lemma:collinearorder
COrpB  lemma:collinearorder
COABF  lemma:collinear5
NCqCr  lemma:NCorder
COqFC  defn:collinear
COqCF  lemma:collinearorder
EQCC  cn:equalityreflexive
COqCC  defn:collinear
NEFC  lemma:betweennotequal
NCFCr  lemma:NChelper
NCFrC  lemma:NCorder
COABr
COABp
COprA lemma:collinearorder
COprF lemma:collinearorder
NEpr  lemma:betweennotequal
COrAF lemma:collinear4 
COFrA lemma:collinearorder
COBAr  lemma:collinearorder
COBAp lemma:collinearorder
COABr lemma:collinearorder
COABp lemma:collinearorder
COprB lemma:collinearorder
COrBF lemma:collinear4
COFrB lemma:collinearorder
NCABC  lemma:NChelper
SSCdAB  defn:sameside
MEABCd  assumption
 ANNEAB+NECd+COABK+COCdK  defn:meet
 NEAB
 COABK
 COCdK
 COCdc  lemma:collinearorder
 NECd lemma:betweennotequal
 COdcK lemma:collinear4
 COcdK lemma:collinearorder
 MEABcd  defn:meet
 NOMEABcd
NOMEABCd reductio
NECd  lemma:betweennotequal
TPABCd   defn:tarski_parallel

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