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PGABCD
COADE
PRABCD  defn:parallelogram
NCABC  lemma:parallelNC
TRABC  defn:triangle
cases ETABCEBC:EQAE|NEAE
 case 1:EQAE
  ETABCABC lemma:ETreflexive
  ETABCEBC cn:equalitysub
 qedcase
 case 2:NEAE
  PRADBC  defn:parallelogram
  CODAE  lemma:collinearorder
  PRBCAD lemma:parallelsymmetric
  PRBCDA lemma:parallelflip
  NEEA  lemma:inequalitysymmetric
  PRBCEA lemma:collinearparallel
  PRBCAE lemma:parallelflip
  PRAEBC lemma:parallelsymmetric
  ETABCEBC  proposition:37
 qedcase
ETABCEBC cases

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