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PGABCD
PGEBCF
BEADF
COAEF
ANPRABCD+PRADBC  defn:parallelogram
ANPREBCF+PREFBC  defn:parallelogram
PRABCD
PRADBC
PREBCF
PREFBC
PRABDC  lemma:parallelflip
PREBFC   lemma:parallelflip
EEADBC   proposition:34
EEEFBC   proposition:34
EEBCEF   lemma:congruencesymmetric
EEADEF   lemma:congruencetransitive
COADF   defn:collinear
COFAE   lemma:collinearorder
COFAD   lemma:collinearorder
NEAF  lemma:betweennotequal
NEFA  lemma:inequalitysymmetric
COAED  lemma:collinear4
ANBEAMC+BEBMD  lemma:diagonalsmeet
BEAMC
BEBMD
BEDMB  axiom:betweennesssymmetry
BEBMD  axiom:betweennesssymmetry
ANBEEmC+BEBmF  lemma:diagonalsmeet
NCADB  lemma:parallelNC
COADF  defn:collinear
EQAA  cn:equalityreflexive
COADA  defn:collinear
NCAFB lemma:NChelper
ANBEBQF+BEAMQ  postulate:Pasch-outer
BEBQF
BEAMQ
COAMQ  defn:collinear
COAMC  defn:collinear
COMAQ  lemma:collinearorder
COMAC  lemma:collinearorder
NEAM  lemma:betweennotequal
NEMA  lemma:inequalitysymmetric
COAQC lemma:collinear4
EQAA  cn:equalityreflexive
EQCC cn:equalityreflexive
COFAA defn:collinear
COCCB defn:collinear
NEAF  lemma:betweennotequal
NEFA  lemma:inequalitysymmetric
NEBC  defn:parallel
NECB  lemma:inequalitysymmetric
MEFACB  assumption
 ANNEFA+NECB+COFAp+COCBp defn:meet
 NEFA
 COFAp
 COCBp
 COADF  defn:collinear
 COFAD  lemma:collinearorder
 NEAD lemma:betweennotequal
 COADp  lemma:collinear4
 COBCp lemma:collinearorder
 ANNEAD+NEBC+COADp+COBCp
 MEADBC  defn:meet
 NOMEADBC defn:parallel
NOMEFACB reductio
BEFQB  axiom:betweennesssymmetry
COACQ  lemma:collinearorder
BEAQC  lemma:collinearbetween
BECQA  axiom:betweennesssymmetry
EQAE assumption
 EEAFAF  cn:congruencereflexive
 EEAFEF  cn:equalitysub
 EEADEF 
 EEEFAD  lemma:congruencesymmetric
 EEAFAD  lemma:congruencetransitive
 EEADAF  lemma:congruencesymmetric
 BEADF
 EEADAD  cn:congruencereflexive
 LTADAF  defn:lessthan
 LTAFAF  lemma:lessthancongruence2
 NOLTAFAF lemma:trichotomy2
NEAE reductio
BEAFE  assumption
 BEEFA axiom:betweennesssymmetry
 NCADC  lemma:parallelNC
 COADE  lemma:collinearorder
 NEAE
 NCAEC  lemma:NChelper
 NCCAE  lemma:NCorder
 ANBECrF+BEErQ  postulate:Pasch-inner
 BECrF
 BEErQ
 BEFQB
 NCEBF  lemma:parallelNC
 NCFBE  lemma:NCorder
 ANBEEHB+BEFrH postulate:Pasch-outer
 BEEHB
 BEFrH
 COEHB  defn:collinear
 COFrH  defn:collinear
 COEBH   lemma:collinearorder
 COCrF  defn:collinear
 COrFC  lemma:collinearorder
 COrFH  lemma:collinearorder
 NErF  lemma:betweennotequal
 COFCH  lemma:collinear4
 PREBFC
 NEBE  lemma:NCdistinct
 NEEB  lemma:inequalitysymmetric
 NEFC   defn:parallel
 ANNEEB+NEFC+COEBH+COFCH
 MEEBFC  defn:meet
 NOMEEBFC  defn:parallel
NOBEAFE  reductio
COAFE  lemma:collinearorder
OREQAF|EQAE|EQFE|BEFAE|BEAFE|BEAEF  defn:collinear
cases BEAEF:EQAF|EQAE|EQFE|BEFAE|BEAFE|BEAEF
 case 1:EQAF
  NOBEAEF assumption
   BEADF
   BEADA  cn:equalitysub
   NOBEADA axiom:betweennessidentity
  BEAEF reductio
 qedcase
 case 2:EQAE
  NOBEAEF assumption
   NEAE
  BEAEF reductio
 qedcase
 case 3:EQFE
  NOBEAEF assumption
   EQEF  lemma:equalitysymmetric
   COBEF  defn:collinear
   COEBF  lemma:collinearorder
   EQFF   cn:equalityreflexive
   COFCF  defn:collinear
   NEEB  defn:parallel
   NEFC  defn:parallel
   ANNEEB+NEFC+COEBF+COFCF
   MEEBFC   defn:meet 
   NOMEEBFC defn:parallel
  BEAEF reductio
 qedcase
 case 4:BEFAE
  NOBEAEF assumption
   EEADAD  cn:congruencereflexive
   LTADAF  defn:lessthan
   EEADDA  cn:equalityreverse
   LTDAAF  lemma:lessthancongruence2
   EEAFFA  cn:equalityreverse
   LTDAFA  lemma:lessthancongruence
   EEFAFA  cn:congruencereflexive
   LTFAFE   defn:lessthan
   LTDAFE   lemma:lessthantransitive
   EEDAFE   lemma:congruenceflip
   LTFEFE   lemma:lessthancongruence2
   NOLTFEFE  lemma:trichotomy2
  BEAEF reductio
 qedcase
 case 5:BEAFE
  NOBEAEF assumption
   NOBEAFE
  BEAEF reductio
 qedcase
 case 6:BEAEF
  BEAEF
 qedcase
BEAEF cases