Sindbad~EG File Manager

TGAaCcBb
EEFGBb
RAFGM
EEFMAa
RAGFN
EEGNCc
ANBEAaJ+EEaJCc+LTBbAJ  defn:togethergreater
BEAaJ
EEaJCc
NEaJ lemma:betweennotequal
NECc  axiom:nocollapse
EQMN assumption
 RAGFN
 RAFGN   cn:equalitysub
 RAGFM  cn:equalitysub
 BEFMG   lemma:tworays
 EEGMCc  cn:equalitysub
 EEMGCc  lemma:congruenceflip
 LTFGFG  lemma:together
 NOLTFGFG lemma:trichotomy2
NEMN  reductio
NEFM  lemma:raystrict
NEMF  lemma:inequalitysymmetric
ANBEMFD+EEFDMF  lemma:extension
BEMFD
RAFGM
ORBEFMG|EQGM|BEFGM  lemma:ray1
cases BEGFD:BEFMG|EQGM|BEFGM
 case 1:BEFMG
  BEGMF   axiom:betweennesssymmetry
  BEMFD
  BEGFD  lemma:3.7a
 qedcase
 case 2:EQGM
  BEMFD
  BEGFD  cn:equalitysub
 qedcase
 case 3:BEFGM
  BEMGF axiom:betweennesssymmetry
  BEMFD
  BEGFD  lemma:3.6a
 qedcase
BEGFD cases
BEDFM axiom:betweennesssymmetry
BEDFG axiom:betweennesssymmetry
BEFMN   assumption
 NEFM   lemma:betweennotequal
 NECc
 ANBEFMP+EEMPCc  lemma:extension
 BEFMP  
 EEFMAa
 EEMPCc
 EEFGBb
 LTFGFP   lemma:together
 EECcGN  lemma:congruencesymmetric
 EECcNG  lemma:congruenceflip
 EEMPNG  lemma:congruencetransitive
 EEFMFM  cn:congruencereflexive
 LTFMFN  defn:lessthan
 BEFMP
 EEMPNG
 BEFNG  assumption
  LTFPFG  lemma:lessthanadditive
  LTFGFP
  LTFGFG  lemma:lessthantransitive
  NOLTFGFG lemma:trichotomy2
 NOBEFNG  reductio
 BEGNF  assumption
  BEFNG axiom:betweennesssymmetry
 NOBEGNF reductio
 BEFMN
 RAGFN
 ORBEGNF|EQFN|BEGFN  lemma:ray1
 OREQFN|BEGFN
 NEFN  lemma:betweennotequal
 NOBEGFN  assumption
  ANNEFN+NOBEGFN
 BEGFN reductio
 BENFG axiom:betweennesssymmetry
 BEDFM
 BEDFG
 NOBENFM  assumption
  BEFMG  assumption
   BENFG
   BENFM axiom:innertransitivity
  NOBEFMG  reductio
  BEFGM  assumption
   BENFG 
   BENFM  lemma:3.7b
  NOBEFGM reductio
  EQGM  lemma:outerconnectivity
  BENFM  cn:equalitysub
 BENFM  reductio
 BEFMN 
 BENFN  lemma:3.7b
 NOBENFN axiom:betweennessidentity
NOBEFMN reductio
COGFN   lemma:rayimpliescollinear
COFGM   lemma:rayimpliescollinear
COGFM   lemma:collinearorder
NEFG  lemma:betweennotequal
NEGF  lemma:inequalitysymmetric
COFNM  lemma:collinear4
COMFN  lemma:collinearorder
OREQMF|EQMN|EQFN|BEFMN|BEMFN|BEMNF  defn:collinear
cases RAMFN:EQMF|EQMN|EQFN|BEFMN|BEMFN|BEMNF
 case 1:EQMF
  NORAMFN assumption
   NEMF
  RAMFN reductio
 qedcase
 case 2:EQMN
  NORAMFN assumption
   NEMN
  RAMFN reductio
 qedcase
 case 3:EQFN
  EQNF   lemma:equalitysymmetric
  RAMFN  lemma:ray4
 qedcase
 case 4:BEFMN
  NORAMFN assumption
   NOBEFMN
  RAMFN reductio
 qedcase
 case 5:BEMFN
  RAMFN lemma:ray4
 qedcase
 case 6:BEMNF
  RAMFN lemma:ray4
 qedcase
RAMFN cases