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EEBCbc
EEADad
EEBDbd
BEABC
BEabc
EEABab
EEACac  axiom:sumofparts
cases EEDCdc:NCacd|COacd
 case 1:NCacd
  EEbcBC  lemma:congruencesymmetric
  EEadAD  lemma:congruencesymmetric
  EEbdBD  lemma:congruencesymmetric
  EEabAB  lemma:congruencesymmetric
  EEdcDC  axiom:5-line
  EEDCdc  lemma:congruencesymmetric
 qedcase
 case 2:COacd
  cases EEDCdc:NCACD|COACD
   case 1:NCACD
    EEDCdc axiom:5-line
   qedcase
   case 2:COACD
    OREQAC|EQAD|EQCD|BECAD|BEACD|BEADC  defn:collinear
    cases EEDCdc:EQAC|EQAD|EQCD|BECAD|BEACD|BEADC
     case 1:EQAC
      NOEEDCdc assumption
       NEAC lemma:betweennotequal
      EEDCdc reductio
     qedcase
     case 2:EQAD
      EQDA   lemma:equalitysymmetric
      EEAAad  cn:equalitysub
      EEadAA  lemma:congruencesymmetric
      EQad   axiom:nullsegment1
      EEDCac  cn:equalitysub
      EEDCdc  cn:equalitysub
      EEDCdc  cn:equalitysub
     qedcase
     case 3:EQCD
      EQDC  lemma:equalitysymmetric
      EECCcc  axiom:nullsegment2
      EEACac
      EEADad
      EEACad  cn:equalitysub
      EEacad  cn:congruencetransitive
      EEBCbc
      EEBDbd
      EEBCbd  cn:equalitysub
      EEbcbd  cn:congruencetransitive
      COacd
      OREQac|EQad|EQcd|BEcad|BEacd|BEadc  defn:collinear
      cases EQcd:EQac|EQad|EQcd|BEcad|BEacd|BEadc
       case 1:EQac
        NEcd assumption
         NEac  lemma:betweennotequal
        EQcd  reductio
       qedcase
       case 2:EQad
        NEAC  lemma:betweennotequal
        NEAD  cn:equalitysub
        NEcd assumption
         NEad  axiom:nocollapse
        EQcd reductio
       qedcase
       case 3:EQcd
        EQcd
       qedcase
       case 4:BEcad
        BEdac  axiom:betweennesssymmetry
        BEabc
        BEdab  lemma:3.6b
        
         
    
    EECCcd  cn:equalitysub
    EQcd   axiom:nullsegment1
    EEDCdc  cn:equalitysub
   qedcase
   case 4:BECAD
    BEDAC axiom:betweennesssymmetry
    EEDAda lemma:congruenceflip
    EEDCdc axiom:sumofparts
   qedcase
   case 5:BEACD
    BECDcd axiom:differenceofparts
    BECDdc axiom:congruenceflip
   qedcase
   case 6:BEADC
    BEDCdc  axiom:differenceofparts
   qedcase
  EEBDCdc cases
 qedcase
EEDCdc cases

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