Sindbad~EG File Manager

CIJDPQ
ONAJ
ONBJ
BEAEB
EEDADB lemma:radiiequal
BEBEA axiom:betweennesssymmetry
EQDD  cn:equalityreflexive
ICDJ  defn:inside
cases ICEJ:EQED|NEED
 case 1:EQED
  EQDE  lemma:equalitysymmetric
  ICEJ  cn:equalitysub
 qedcase
 case 2:NEED
  ANCOEDF+BEEDC+ONFJ+ONCJ+BEFDC postulate:line-circle
  COEDF
  BEEDC
  ONFJ
  ONCJ
  BEFDC  
  cases ICEJ:NCDAB|CODAB
   case 1:NCDAB
    TRDAB    defn:triangle
    ISDAB    defn:isosceles
    EADABDBA proposition:05
    NEAE  lemma:betweennotequal
    NEEB  lemma:betweennotequal
    NEBE  lemma:inequalitysymmetric
    NEAB  lemma:betweennotequal
    NEBA  lemma:inequalitysymmetric
    RAABE  lemma:ray4
    RABAE  lemma:ray4
    EQAA   cn:equalityreflexive
    EQBB   cn:equalityreflexive
    EQDD   cn:equalityreflexive
    RABAA  lemma:ray4
    RAABB  lemma:ray4
    NEBD   lemma:NCdistinct
    NEAD   lemma:NCdistinct
    RABDD  lemma:ray4
    RAADD  lemma:ray4
    EADABDBE  lemma:equalangleshelper
    EADBEDAB  lemma:equalanglessymmetric
    EADBEDAE  lemma:equalangleshelper
    NCABD   lemma:NCorder
    COAEB   defn:collinear
    COABE   lemma:collinearorder
    COABA  defn:collinear
    NCAED   lemma:NChelper
    NCDAE   lemma:NCorder
    TRDAE     defn:triangle
    AOEADDEB proposition:16
    EADAEEAD  lemma:ABCequalsCBA
    AODAEDEB  lemma:angleorderrespectscongruence2
    AODBEDEB lemma:angleorderrespectscongruence2
    NCDBE   lemma:equalanglesNC
    NCEBD   lemma:NCorder
    EAEBDDBE  lemma:ABCequalsCBA
    AOEBDDEB  lemma:angleorderrespectscongruence2
    NCABD   lemma:NCorder
    COABE    lemma:collinearorder
    EQBB      cn:equalityreflexive
    COABB     defn:collinear
    NEEB   lemma:betweennotequal
    NCEBD   lemma:NChelper
    NCDEB   lemma:NCorder
    TRDEB   defn:triangle
    LTDEDB   proposition:19
    EEDBDF lemma:radiiequal
    LTDEDF  lemma:lessthancongruence
    BEDFE assumption
     EEDFDF  cn:congruencereflexive
     LTDFDE  defn:lessthan
     NOLTDEDF  lemma:trichotomy2
    NOBEDFE  reductio  % Therefore the straight line AB will not fall outside the circle
    EQFE  assumption   
     EEDEDE cn:congruencereflexive
     EEDEDF cn:equalitysub
     LTDFDF  lemma:lessthancongruence2
     NOLTDFDF  lemma:trichotomy2
    NEFE   reductio
    COEDF
    BEFDC
    BEEDC
    OREQED|EQEF|EQDF|BEDEF|BEEDF|BEEFD  defn:collinear
    NEFD  lemma:betweennotequal
    cases ICEJ:EQED|EQEF|EQDF|BEDEF|BEEDF|BEEFD
     case 1:EQED
      NOICEJ assumption 
       NEED lemma:betweennotequal
      ICEJ reductio
     qedcase
     case 2:EQEF
      NOICEJ assumption
       NEEF lemma:inequalitysymmetric
      ICEJ reductio
     qedcase
     case 3:EQDF
      NOICEJ assumption
       NEDF lemma:inequalitysymmetric
      ICEJ reductio
     qedcase
     case 4:BEDEF
      EEDEDE cn:congruencereflexive
      EEDFPQ axiom:circle-center-radius
      ANBEDEF+EEDFPQ+EEDEDE
      ICEJ  defn:inside
    qedcase
     case 5:BEEDF
      BECDF axiom:betweennesssymmetry
      BECDE axiom:betweennesssymmetry
      NOBEDEF assumption
       EQEF  lemma:outerconnectivity
       NEEF lemma:betweennotequal
      BEDEF  reductio
      BEFED  axiom:betweennesssymmetry
      BEFDE  axiom:betweennesssymmetry
      BEEDE  lemma:3.6a
      NOICEJ assumption
       NOBEEDE axiom:betweennessidentity
      ICEJ  reductio
     qedcase
     case 6:BEEFD
      BEDFE  axiom:betweennesssymmetry
      NOICEJ assumption
       NOBEDFE
      ICEJ reductio
     qedcase
    ICEJ cases
   qedcase
   case 2:CODAB   
    COABD  lemma:collinearorder
    NEAB   lemma:betweennotequal
    EEADDB lemma:congruenceflip
    BEADB  lemma:collinearmidpoint
    BEAEB
    EEDBPQ  axiom:circle-center-radius
    EEDAPQ  axiom:circle-center-radius
    ICEJ   lemma:ondiameter
   qedcase
  ICEJ cases
 qedcase
ICEJ cases