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PGABCD
PRABCD  defn:parallelogram
PRADBC  defn:parallelogram
ANNEAB+NECD+COABa+COABb+NEab+COCDc+COCDd+NEcd+NOMEABCD+BEamd+BEcmb defn:parallel
NEAB
NECD
NOMEABCD
NOMEADBC defn:parallel
PRCDAB  lemma:parallelsymmetric
TPCDAB lemma:paralleldef2B
SSABCD  defn:tarski_parallel
EQDD  cn:equalityreflexive
CODCD  defn:collinear
EQAD assumption
 CODCA  cn:equalitysub
 COCDA  lemma:collinearorder
 EQAA  cn:equalityreflexive
 COABA  defn:collinear
 MEABCD  defn:meet
NEAD reductio
ANBEADE+EEDEAD lemma:extension
BEADE
CODCA  assumption
 EQAA  cn:equalityreflexive
 COABA defn:collinear
 COCDA lemma:collinearorder
 MEABCD  defn:meet
 NOMEABCD defn:parallel
NCDCA reductio
OSADCE    defn:oppositeside
SSABCD
SSBADC  lemma:samesidesymmetric
OSBDCE  lemma:planeseparation
ANBEBFE+CODCF+NCDCB   defn:oppositeside
BEBFE
CODCF
NCDCB
BEEFB  axiom:betweennesssymmetry
BEEDA  axiom:betweennesssymmetry
COEDA  defn:collinear
NEED  lemma:betweennotequal
NEEA  lemma:betweennotequal
EQBC assumption
 CODBC defn:collinear
 CODCB lemma:collinearorder
NEBC reductio
ANBEBCS+EECSBC  lemma:extension
BEBCS
BESCB  axiom:betweennesssymmetry
COSCB  defn:collinear
NESB  lemma:betweennotequal
NECB  lemma:betweennotequal
MEEASB  assumption
 ANNEEA+NESB+COEAR+COSBR defn:meet
 NEEA
 NESB
 COEAR
 COSBR
 COBCS  defn:collinear
 COSBC  lemma:collinearorder
 cases COBCR:EQBR|NEBR
  case 1:EQBR
   COBCR defn:collinear
  qedcase
  case 2:NEBR
   COBRC  lemma:collinear4
   COBCR lemma:collinearorder
  qedcase
 COBCR cases
 COADE defn:collinear
 COEAD  lemma:collinearorder
 NEAD lemma:betweennotequal
 COADR lemma:collinear4
 ANNEAD+NEBC+COADR+COBCR
 MEADBC  defn:meet
NOMEEASB reductio
BEDFC  lemma:collinearbetween
BECFD  axiom:betweennesssymmetry
NEAE lemma:betweennotequal
NEEA  lemma:inequalitysymmetric
NEBS  lemma:betweennotequal
NESB  lemma:inequalitysymmetric
COEAC  assumption
 COBCS  defn:collinear
 COSBC  lemma:collinearorder
 ANNEEA+NESB+COEAC+COSBC
 MEEASB defn:meet
 NOMEEASB
NCEAC reductio
ANBECHA+BEEFH  postulate:Pasch-outer
BECHA
BEEFH
COEFH defn:collinear
COEFB defn:collinear
NEEF  lemma:betweennotequal
NEFE  lemma:inequalitysymmetric
COFEH lemma:collinearorder
COFEB lemma:collinearorder
COEHB lemma:collinear4
BEAHC  axiom:betweennesssymmetry
NEAE
ANBEAER+EEERAE  lemma:extension
BEAER
COAER  defn:collinear
NEAE  lemma:betweennotequal
NEAR  lemma:betweennotequal
NECB lemma:inequalitysymmetric
ANBECBT+EEBTCB lemma:extension
BECBT
MEARTC assumption
 ANNEAR+NETC+COARp+COTCp defn:meet
 NEAR
 NETC
 COARp
 COTCp
 COCBT  defn:collinear
 COADE  defn:collinear
 EQAA   cn:equalityreflexive
 COARA  defn:collinear
 COEAD  lemma:collinearorder
 COAER  defn:collinear
 COEAR  lemma:collinearorder
 NEAD  lemma:betweennotequal
 COADR  lemma:collinear4
 COARD  lemma:collinearorder
 COADp  lemma:collinear5
 COBTC  lemma:collinearorder
 COTCB  lemma:collinearorder
 NECT  lemma:betweennotequal
 NETC  lemma:inequalitysymmetric
 COCBp  lemma:collinear4
 COBCp  lemma:collinearorder
 ANNEAD+NEBC+COADp+COBCp
 MEADBC defn:meet
 NOMEADBC
NOMEARTC reductio
BETBC  axiom:betweennesssymmetry
COTBC  defn:collinear
NETC  lemma:betweennotequal
NEBC  lemma:betweennotequal
BEAHC
COEBH  lemma:collinearorder
BEEHB  lemma:collinearbetween
BEBHE  axiom:betweennesssymmetry
BEADE
COBEA assumption
 COADE defn:collinear
 COEAD lemma:collinearorder
 COEAB lemma:collinearorder
 COADB lemma:collinear4
 EQBB  cn:equalityreflexive
 COBCB  defn:collinear
 ANNEAD+NEBC+COADB+COBCB
 MEADBC  defn:meet
NCBEA reductio
ANBEBMD+BEAMH  postulate:Pasch-inner
BEBMD
BEAMH
BEAHC  axiom:betweennesssymmetry
BEAMC  lemma:3.6b
ANBEAMC+BEBMD