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PRABCD
PRABCE
NOORCRADBC|CRACBD  assumption 
 ANNOCRADBC+NOCRACBD
 NOCRADBC
 NOCRACBD
 PRABDC  lemma:parallelflip
 CRACDB lemma:crisscross
 ANBEApC+BEDpB  defn:cross
 BEApC
 BEDpB
 BEBpD  axiom:betweennesssymmetry
 ANBEApC+BEBpD
 CRACBD defn:cross
ORCRADBC|CRACBD reductio
cases COCDE:CRADBC|CRACBD
 case 1:CRADBC
  COCDE lemma:Playfairhelper2
 qedcase
 case 2:CRACBD
  ANBEApC+BEBpD defn:cross
  BEApC
  BEBpD
  ANBEBpD+BEApC
  CRBDAC defn:cross
  PRBACD  lemma:parallelflip
  PRBACE   lemma:parallelflip
  COCDE lemma:Playfairhelper2
 qedcase
COCDE cases

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