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TPABcd
BEcCd
ANNEAB+NEcd+NOMEABcd+SScdAB  defn:tarski_parallel
NEAB
NEcd
SScdAB
ANCOABp+COABr+BEcpq+BEdrq+NCABc+NCABd  defn:sameside
COABp
COABr
BEcpq
BEdrq
NECd lemma:betweennotequal
BEqrd  axiom:betweennesssymmetry
BEdCc axiom:betweennesssymmetry
BEqpc axiom:betweennesssymmetry
COqpc defn:collinear
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
NCABc
NCABd
NCprc lemma:NChelper
NCprd lemma:NChelper
NCrdp  lemma:NCorder
COqrd  defn:collinear
COrdq lemma:collinearorder
EQdd  cn:equalityreflexive
COrdd  defn:collinear
NEqd lemma:betweennotequal
NCqdp  lemma:NChelper
NCqpd lemma:NCorder
EQcp assumption
 EQpc lemma:equalitysymmetric
 COprc defn:collinear
 NCprc
NEcp reductio
COqpc
EQpp cn:equalityreflexive
COqpp defn:collinear
NCcpd lemma:NChelper
COcpq  lemma:collinearorder
EQcc  cn:equalityreflexive
COcpc  defn:collinear
NEqc lemma:betweennotequal
NCqcd  lemma:NChelper
BEqpc axiom:betweennesssymmetry
ANBEqEC+BEdEp  postulate:Pasch-inner
BEdEp
BEpEd  axiom:betweennesssymmetry
BEqrd  axiom:betweennesssymmetry
NCqdp
ANBEqFE+BEpFr postulate:Pasch-inner
BEpFr
COprF defn:collinear
COBrp lemma:collinear4
COBAp lemma:collinearorder
NEBA lemma:inequalitysymmetric
COBpr lemma:collinearorder
COBpA lemma:collinearorder
COABC  assumption
 COcCd defn:collinear
 COcdC lemma:collinearorder
 NEcd 
 NEAB
 MEABcd defn:meet
 NOMEABcd
NCABC reductio
BEqEC
BEqFE
BEqFC lemma:3.6b
BECFq  axiom:betweennesssymmetry
BEdrq
NOSSCdAB assumption
 NEBp assumption
  COprA  lemma:collinear4
  COApr lemma:collinearorder
  COApB lemma:collinearorder
  BEdrq
  COABr 
  NEAp assumption
   COprB lemma:collinear4
   COABF lemma:collinear5
   SSCdAB defn:sameside
  EQAp reductio
  COArF cn:equalitysub
  COrAF  lemma:collinearorder
  COrAB  lemma:collinearorder
  EQrA assumption
   EQrp cn:equalitysub
   NEpr lemma:betweennotequal   
   NErp lemma:inequalitysymmetric
  NErA reductio
  COAFB lemma:collinear4
  COABF lemma:collinearorder
  SSCdAB defn:sameside
 EQBp reductio
 NEAp cn:equalitysub
 EQAA  cn:equalityreflexive
 COBAA defn:collinear
 COBAp  lemma:collinearorder
 COBAr lemma:collinearorder
 COApr lemma:collinear5
 COprB lemma:collinearorder
 COprA lemma:collinearorder
 COABF lemma:collinear5
 SSCdAB defn:sameside
SSCdAB reductio
MEABCd  assumption
 ANNEAB+NECd+COABR+COCdR  defn:meet
 COABR
 COCdR
 COcCd  defn:collinear
 COCdc lemma:collinearorder
 NECd lemma:betweennotequal
 COdcR lemma:collinear4
 COcdR lemma:collinearorder
 MEABcd defn:meet
 NOMEABcd
NOMEABCd reductio
ANNEAB+NECd+NOMEABCd+SSCdAB
TPABCd  defn:tarski_parallel

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