Sindbad~EG File Manager

PGABCD
PGEBCF
BEADF
COAEF
ANPRABCD+PRADBC  defn:parallelogram
PRABCD
PRADBC
PRABDC  lemma:parallelflip
EEADBC   proposition:34
EEEFBC   proposition:34
EEBCEF   lemma:congruencesymmetric
EEADEF   lemma:congruencetransitive
EEEFFE  cn:equalityreverse
EEADFE  lemma:congruencetransitive
EEADAD  cn:congruencereflexive
LTADAF   defn:lessthan
LTFEAF   lemma:lessthancongruence2
EEAFFA   cn:equalityreverse
LTFEFA   lemma:lessthancongruence
ANBEFeA+EEFeFE  defn:lessthan
BEFeA
EEFeFE 
NEFA  lemma:betweennotequal
RAFAe  lemma:ray4 
BEAEF   lemma:35helper
BEFEA axiom:betweennesssymmetry
RAFAE lemma:ray4
EQeE    lemma:layoffunique
BEFEA  cn:equalitysub
BEAEF  axiom:betweennesssymmetry
PRDCAB  lemma:parallelsymmetric
BEFDA   axiom:betweennesssymmetry
TPADBC  lemma:paralleldef2B
SSBCAD  defn:tarski_parallel
SSCBDA  lemma:samesidesymmetric
EAFDCDAB  proposition:29C
EQDD   cn:equalityreflexive
EQCC   cn:equalityreflexive
EQBB   cn:equalityreflexive
EQAA   cn:equalityreflexive
NCADC  lemma:parallelNC
EQAD assumption
 COADC defn:collinear
NEAD reductio
NEAD lemma:betweennotequal
NCABC  lemma:parallelNC
EQAB assumption
 COABC defn:collinear
NEAB reductio
RAABB lemma:ray4
NOORBEADE|BEAED|EQDE  assumption
 ANNOBEADE+NOBEAED+NEDE
 NOBEADE
 NOBEAED
 NEDE
 BEADF  
 BEAEF
 EQDE axiom:connectivity
ORBEADE|BEAED|EQDE  reductio
cases RAADE:BEADE|BEAED|EQDE
 case 1:BEADE
  RAADE  lemma:ray4 
 qedcase
 case 2:BEAED
  RAADE  lemma:ray4
 qedcase
 case 3:EQDE
  NEAD
  RAADD  lemma:ray4
  RAADE cn:equalitysub
 qedcase
RAADE cases
NCADB  lemma:parallelNC
NCDAB  lemma:NCorder
EADABDAB  lemma:equalanglesreflexive
EADABEAB  lemma:equalangleshelper
EAFDCEAB  lemma:equalanglestransitive
EEABDC    proposition:34
EEDEED  cn:equalityreverse
cases EEAEDF:BEADE|BEAED|EQDE
 case 1:BEADE
   % the only case Euclid treats
  BEDEF  lemma:3.6a
  BEFED  axiom:betweennesssymmetry
  EEAEFD  cn:sumofparts
  EEAEDF  lemma:congruenceflip
 qedcase
 case 2:BEAED
  BEDEA  axiom:betweennesssymmetry
  BEEDF  lemma:3.6a
  EEADFE
  EEDAEF  lemma:congruenceflip
  EEEADF  lemma:differenceofparts
  EEAEDF  lemma:congruenceflip
 qedcase
 case 3:EQDE
  EEADEF
  EEAEEF   cn:equalitysub
  EEAEDF   cn:equalitysub
 qedcase
EEAEDF cases
EEDFAE lemma:congruencesymmetric
EEDCAB  lemma:congruencesymmetric
ANEEFCEB+EADFCAEB+EADCFABE proposition:04
EEFCEB
EEFDEA  lemma:congruenceflip
EADCFABE  
EAABEDCF  lemma:equalanglessymmetric
NCDCF lemma:equalanglesNC
NCFDC lemma:NCorder
TRFDC  defn:triangle
ANEEFDEA+EEDCAB+EEFCEB+TRFDC
TCFDCEAB  defn:trianglecongruence
ETFDCEAB  axiom:congruentequal
cases EFABCDEBCF:BEADE|BEAED|EQDE
 case 1:BEADE
  PGABCD
  ANBEAMC+BEBMD  lemma:diagonalsmeet
  BEBMD
  BEDMB  axiom:betweennesssymmetry
  NCADB   lemma:parallelNC
  COADE   defn:collinear
  COADA   defn:collinear
  NEAE   lemma:betweennotequal
  NCAEB   lemma:NChelper
  BEBMD  axiom:betweennesssymmetry
  BEAMC
  ANBEBHE+BEAMH  postulate:Pasch-outer
  BEBHE
  BEAMH
  COAMH  defn:collinear
  COAMC  defn:collinear
  NEAM lemma:betweennotequal
  NEMA  lemma:inequalitysymmetric
  COMAH  lemma:collinearorder
  COMAC  lemma:collinearorder
  COAHC  lemma:collinear4
  BEEHB  axiom:betweennesssymmetry
  NEEA  lemma:inequalitysymmetric
  EQBC assumption
   COABC  defn:collinear
  NEBC  reductio
  NOMEADBC   defn:parallel
  MEEACB  assumption
   ANNEEA+NECB+COEAq+COCBq defn:meet
   NEEA
   NECB
   NEBC  lemma:inequalitysymmetric
   COEAq
   COCBq
   COBCq lemma:collinearorder
   COAEq  lemma:collinearorder
   COADE  defn:collinear
   COEAD  lemma:collinearorder
   COEAq  lemma:collinearorder
   NEAD  lemma:betweennotequal
   COADq  lemma:collinear4
   ANNEAD+NEBC+COADq+COBCq 
   MEADBC  defn:meet
  NOMEEACB reductio
  BEEHB
  COAHC
  COACH lemma:collinearorder
  COEAA  defn:collinear
  COCCB  defn:collinear
  NEEA 
  NEAE 
  NEBC
  NECB lemma:inequalitysymmetric
  BEAHC lemma:collinearbetween
  BECHA  axiom:betweennesssymmetry
  BEEDA axiom:betweennesssymmetry
  NCADC  lemma:parallelNC
  COADE  defn:collinear
  NCAEC  lemma:NChelper
  NCCAE  lemma:NCorder
  ANBECGD+BEEGH postulate:Pasch-inner
  BEEGH
  BEEHB
  BEEGB  lemma:3.6b
  BEEGH
  BEEHB
  BEEGB  lemma:3.6b
  COEGB  defn:collinear
  CODEG  assumption
   COGED  lemma:collinearorder
   COGEB  lemma:collinearorder
   NEEG  lemma:betweennotequal
   NEGE  lemma:inequalitysymmetric
   COEDB  lemma:collinear4
   COBCB  defn:collinear
   COEDA  lemma:collinearorder
   COEDD  defn:collinear
   NEDE  lemma:betweennotequal
   NEED  lemma:inequalitysymmetric
   COADB  lemma:collinear5
   ANNEAD+NEBC+COADB+COBCB
   MEADBC  defn:meet
   NOMEADBC
  NCDEG reductio
  TRDEG  defn:triangle
  ETDEGDEG lemma:ETreflexive
  ETDEGEDG axiom:ETpermutation 
  ETFDCEAB 
  ETFDCAEB axiom:ETpermutation
  ETAEBFDC axiom:ETsymmetric
  BEBGE   axiom:betweennesssymmetry
  BECGD
  BEADE
  BEDEF  lemma:3.6a
  BEFED  axiom:betweennesssymmetry
  EFADGBFEGC   axiom:cutoff1
  NCDEG
  NCEGD   lemma:NCorder
  COEGB 
  EQGG    cn:equalityreflexive
  COEGG   defn:collinear  
  NEGB   lemma:betweennotequal
  NEBG    lemma:inequalitysymmetric
  NCBGD   lemma:NChelper
  NCDGB   lemma:NCorder
  COCGD  defn:collinear
  CODGC   lemma:collinearorder
  CODGG   defn:collinear
  NECG   lemma:betweennotequal
  NCCGB   lemma:NChelper
  NCGCB    lemma:NCorder
  TRGCB      defn:triangle
  ETGCBGCB   lemma:ETreflexive
  ETGCBGBC   axiom:ETpermutation
  EFADGBFEGC
  BECGD 
  BEDGC    axiom:betweennesssymmetry 
  PGBCDA  lemma:PGrotate
  PGDABC  lemma:PGsymmetric
  PGADCB   lemma:PGflip
  ANBEAqC+BEDqB lemma:diagonalsmeet
  BEAqC
  BEDqB
  PGBCFE  lemma:PGrotate
  PGCFEB  lemma:PGrotate
  PGFEBC  lemma:PGrotate
  ANBEFmB+BEEmC lemma:diagonalsmeet
  BEFmB
  BEEmC 
  EFADCBFEBC   axiom:paste2
  EFADCBEBCF   axiom:EFpermutation
  EFEBCFADCB  axiom:EFsymmetric
  EFEBCFABCD  axiom:EFpermutation
  EFABCDEBCF  axiom:EFsymmetric
 qedcase
 case 2:BEAED
  ETFDCEAB
  ETEABFDC   axiom:ETsymmetric
  ETEABDFC   axiom:ETpermutation
  ANBEBHD+BECHE  lemma:trapezoiddiagonals
  BEBHD
  BECHE
  BEEHC       axiom:betweennesssymmetry
  COBED   assumption
   COAED   defn:collinear
   COEDA   lemma:collinearorder
   COEDB   lemma:collinearorder
   NEED    lemma:betweennotequal
   CODAB    lemma:collinear4
   COADB    lemma:collinearorder
   EQBB     cn:equalityreflexive
   COBCB    defn:collinear
   NEAD     defn:parallel
   NEBC     defn:parallel
   MEADBC   defn:meet
   NOMEADBC   defn:parallel 
  NCBED    reductio
  EFBEDCBEDC  lemma:EFreflexive
  EFBEDCCDEB  axiom:EFpermutation
  EFCDEBBEDC  axiom:EFsymmetric 
  BEDEA    axiom:betweennesssymmetry
  BEEDF    lemma:3.6a
  PGCDAB   lemma:PGsymmetric
  ANBECpA+BEDpB  lemma:diagonalsmeet
  BECpA
  BEDpB
  PGBEFC    lemma:PGflip
  ANBEBmF+BEEmC  lemma:diagonalsmeet
  BEBmF
  BEEmC 
  EFCDABBEFC  axiom:paste2
  EFCDABEBCF  axiom:EFpermutation
  EFEBCFCDAB  axiom:EFsymmetric
  EFEBCFABCD  axiom:EFpermutation
  EFABCDEBCF  axiom:EFsymmetric
 qedcase
 case 3: EQDE
  ETFDCEAB
  ETFDCBEA   axiom:ETpermutation
  ETBEAFDC   axiom:ETsymmetric
  ETBEACDF   axiom:ETpermutation
  NCDBC     lemma:parallelNC
  NCEBC     cn:equalitysub
  NCBEC     lemma:NCorder
  TRBEC     defn:triangle
  ETBECBEC   lemma:ETreflexive
  ETBECCEB   axiom:ETpermutation
  ETBECCDB   cn:equalitysub
  PGABCE    cn:equalitysub
  ANBEAMC+BEBME  lemma:diagonalsmeet
  BEAMC
  BEBME
  BEEMB  axiom:betweennesssymmetry
  COEMB  defn:collinear
  COBEM  lemma:collinearorder
  PRAEBC  defn:parallelogram
  NCAEB  lemma:parallelNC
  NCBEA  lemma:NCorder
  OSABEC  defn:oppositeside
  PGDBCF  cn:equalitysub
  NCCDF   lemma:NCorder
  ANBEDmC+BEBmF  lemma:diagonalsmeet
  BEDmC
  BEBmF
  BEFmB axiom:betweennesssymmetry
  CODmC  defn:collinear
  COCDm  lemma:collinearorder
  OSFCDB defn:oppositeside
  ANBEAJC+BEBJD  lemma:diagonalsmeet
  BEAJC
  BEBJD
  BEBJE   cn:equalitysub
  ANBEEjC+BEBjF  lemma:diagonalsmeet
  BEEjC
  BEDjC   cn:equalitysub
  BECjD  axiom:betweennesssymmetry
  BEBjF 
  BEFjB   axiom:betweennesssymmetry
  EFBAECCFDB  axiom:paste3
  EFBAECDBCF  axiom:EFpermutation
  EFBAECEBCF  cn:equalitysub
  EFEBCFBAEC  axiom:EFsymmetric
  EFEBCFABCE  axiom:EFpermutation
  EFEBCFABCD  cn:equalitysub
  EFABCDEBCF  axiom:EFsymmetric
 qedcase
EFABCDEBCF cases