Sindbad~EG File Manager

RAABC
RAABD
EEACAD
EEADAC  lemma:congruencesymmetric
ORBEACB|EQBC|BEABC  lemma:ray1
ORBEADB|EQBD|BEABD  lemma:ray1
EEABAB  cn:congruencereflexive
EECBCB  cn:congruencereflexive
EEACAC  cn:congruencereflexive
cases EQCD:BEACB|EQBC|BEABC
 case 1:BEACB
  cases EQCD:BEADB|EQBD|BEABD
   case 1:BEADB
    EECBDB lemma:differenceofparts
    EEBCBD lemma:congruenceflip
    EECCCD lemma:interior5
    EECDCC lemma:congruencesymmetric
    NECD  assumption
     NECC  axiom:nocollapse
     EQCC  cn:equalityreflexive
    EQCD reductio
   qedcase
   case 2:EQBD
    BEACD cn:equalitysub
    NECD  assumption
     NOEEACAD lemma:partnotequalwhole
    EQCD  reductio
   qedcase
   case 3:BEABD
    BEACD  lemma:3.6b
    NECD assumption
     NOEEACAD  lemma:partnotequalwhole
    EQCD reductio
   qedcase
  EQCD cases
 qedcase
 case 2:EQBC
  EEABAD  cn:equalitysub
  EEADAB  lemma:congruencesymmetric
  cases EQCD:BEADB|EQBD|BEABD
   case 1:BEADB 
    NECD assumption
     NOEEADAB  lemma:partnotequalwhole
    EQCD reductio
   qedcase
   case 2:EQBD
    EQCB  lemma:equalitysymmetric
    EQDB  lemma:equalitysymmetric
    EQCD  cn:equalitytransitive
   qedcase
   case 3:BEABD
    BEACD   cn:equalitysub
    NECD  assumption
     NOEEACAD lemma:partnotequalwhole
    EQCD reductio
   qedcase
  EQCD cases 
 qedcase
 case 3:BEABC
  cases EQCD:BEADB|EQBD|BEABD
   case 1:BEADB
    BEADC  lemma:3.6b
    NECD  assumption
     NOEEADAC  lemma:partnotequalwhole
    EQCD  reductio
   qedcase
   case 2:EQBD
    BEADC  cn:equalitysub
    NECD  assumption
     NOEEADAC lemma:partnotequalwhole
    EQCD  reductio
   qedcase
   case 3:BEABD
     EEBCBD  lemma:differenceofparts
     EQCD   lemma:extensionunique
   qedcase
  EQCD cases
 qedcase
EQCD cases