Sindbad~EG File Manager

COABC
COABD
NEAB
cases COBCD:EQBC|EQBD|EQCD|EQAC|EQAD|ANNEBC+NEBD+NECD+NEAC+NEAD
 case 1:  EQBC
  COBCD defn:collinear
 qedcase
 case 2: EQBD
  COBCD defn:collinear
 qedcase
 case 3: EQCD
  COBCD defn:collinear
 qedcase
 case 4: EQAC
  COABD
  COCBD  cn:equalitysub
  COBCD  lemma:collinearorder
 qedcase
 case 5: EQAD
  COABC
  CODBC cn:equalitysub
  COBCD lemma:collinearorder
 qedcase
 case 6: ANNEBC+NEBD+NECD+NEAC+NEAD
  NEBC
  NEBD
  NEAC
  NEAD
  OREQAB|EQAC|EQBC|BEBAC|BEABC|BEACB  defn:collinear
  ORBEBAC|BEABC|BEACB
  cases COBCD: BEBAC|BEABC|BEACB
   case 1: BEBAC
    COABD
    OREQAB|EQAD|EQBD|BEBAD|BEABD|BEADB defn:collinear
    ORBEBAD|BEABD|BEADB 
    cases COBCD:BEBAD|BEABD|BEADB 
     case 1: BEBAD
      NCBCD    assumption
       BEBCD    assumption
        COBCD    defn:collinear
        NOBEBCD  reductio
        BEACD    assumption
        BEBCD    lemma:3.5b
       NOBEACD  reductio
       NCBDC    assumption
        BEADC    assumption
         BEBDC    lemma:3.5b
         COBDC    defn:collinear
         NCBDC
         NOBEADC  reductio
        EQCD  lemma:outerconnectivity
        COBCD  defn:collinear
        COBDC  lemma:collinearorder
       COBDC   reductio
       COBCD   lemma:collinearorder
      COBCD  reductio
     qedcase
     case 2: BEABD
      BEDBA  axiom:betweennesssymmetry
      BEDBC  lemma:3.7b
      CODBC  defn:collinear
      COBCD lemma:collinearorder
     qedcase
     case 3: BEADB
      BEBDA   axiom:betweennesssymmetry
      BEBAC
      BEBDC   lemma:3.6b  
      COBDC   defn:collinear
      COBCD   lemma:collinearorder
     qedcase
    COBCD cases
   qedcase
   case 2: BEABC
    COABD  
    OREQAB|EQAD|EQBD|BEBAD|BEABD|BEADB  defn:collinear
    ORBEBAD|BEABD|BEADB 
    cases COBCD:BEBAD|BEABD|BEADB 
     case 1: BEBAD
      BEDAB  axiom:betweennesssymmetry
      BEDBC  lemma:3.7a
      CODBC  defn:collinear
      COBCD  lemma:collinearorder
     qedcase
     case 2: BEABD
      NCBCD  assumption
       BEBCD   assumption
        COBCD   defn:collinear
       NOBEBCD reductio
       BEBDC   assumption
        COBDC   defn:collinear
        COBCD   lemma:collinearorder
        NCBCD
       NOBEBDC  reductio
       EQCD   lemma:outerconnectivity
       COBCD  defn:collinear
      COBCD  reductio
     qedcase
     case 3: BEADB
      BEDBC   lemma:3.6a
      CODBC  defn:collinear
      COBCD  lemma:collinearorder
     qedcase
    COBCD cases
   qedcase
   case 3: BEACB
    COABD
    OREQAB|EQAD|EQBD|BEBAD|BEABD|BEADB  defn:collinear
    ORBEBAD|BEABD|BEADB 
    cases COBCD:BEBAD|BEABD|BEADB 
     case 1: BEBAD
      BEDAB  axiom:betweennesssymmetry
      BEDCB  lemma:3.5b
      BEBCD  axiom:betweennesssymmetry
      COBCD  defn:collinear
     qedcase
     case 2: BEABD
      BEACB
      BECBD   lemma:3.6a
      COBCD   defn:collinear
     qedcase
     case 3: BEADB
      NCBCD  assumption
       NOBEBDC   assumption
        NOBEBCD   assumption
         BEBCA   axiom:betweennesssymmetry
         BEBDA   axiom:betweennesssymmetry
         EQCD    axiom:connectivity
         NECD
        BEBCD reductio
        COBCD   defn:collinear
       BEBDC   reductio
       COBDC   defn:collinear
       COBCD  lemma:collinearorder
      COBCD  reductio
     qedcase
    COBCD cases
   qedcase
  COBCD cases
 qedcase 
COBCD cases