Sindbad~EG File Manager

PGABCD
PGEBCF
COADE
COADF
ANPRABCD+PRADBC  defn:parallelogram
ANPREBCF+PREFBC  defn:parallelogram
PRABCD
PRADBC
PREBCF
PREFBC
PRABDC  lemma:parallelflip
PREBFC   lemma:parallelflip
PRFCEB  lemma:parallelsymmetric
EEADBC   proposition:34
EEEFBC   proposition:34
EEBCEF   lemma:congruencesymmetric
EEADEF   lemma:congruencetransitive
NEAD  defn:parallel
NEEF  defn:parallel
NEDA  lemma:inequalitysymmetric
NOEFABCDEBCF  assumption
 BEADF  assumption 
  COADF  defn:collinear
  COADE
  CODAF  lemma:collinearorder
  CODAE  lemma:collinearorder
  COAFE  lemma:collinear4
  COAEF  lemma:collinearorder
  EFABCDEBCF proposition:35A
 NOBEADF  reductio
 BEADE  assumption
  ANBEBHE+BECHD  lemma:parallelPasch
  BEBHE
  BECHD
  BEDHC  axiom:betweennesssymmetry
  COBHE  defn:collinear
  COBEH  lemma:collinearorder
  NCADB  lemma:parallelNC
  COADE  defn:collinear
  EQDD  cn:equalityreflexive
  COADD  defn:collinear
  NEDE lemma:betweennotequal
  NCDEB  lemma:NChelper
  NCBED  lemma:NCorder
  ANBEDHC+COBEH+NCBED
  OSDBEC  defn:oppositeside
  OSCBED  lemma:oppositesidesymmetric
  PRFCBE  lemma:parallelflip
  PRBEFC   lemma:parallelsymmetric
  TPBEFC lemma:paralleldef2B
  SSFCBE  defn:tarski_parallel
  OSFBED lemma:planeseparation
  ANBEFeD+COBEe+NCBEF  defn:oppositeside
  BEFeD
  NEFD  lemma:betweennotequal
  COFeD  defn:collinear
  NEeE  assumption
   COBEe
   COADE
   COADF
   NEAD   lemma:betweennotequal
   CODEF  lemma:collinear4
   COFDE  lemma:collinearorder
   COFDe  lemma:collinearorder
   CODEe  lemma:collinear4 
   COeED  lemma:collinearorder
   COeEB  lemma:collinearorder
   COEDB  lemma:collinear4
   COBED   lemma:collinearorder
   NCBED
  EQeE  reductio
  BEFED  cn:equalitysub
  BEDEF  axiom:betweennesssymmetry
  BEADE
  BEADF  lemma:3.7b
  NOBEADF
 NOBEADE reductio
 PRBADC  lemma:parallelflip
 PRDCBA  lemma:parallelsymmetric
 PRDACB  lemma:parallelflip
 PGDCBA  defn:parallelogram
 PRBEFC  lemma:parallelflip
 PRFCBE  lemma:parallelsymmetric
 PRFECB   lemma:parallelflip
 PGFCBE  defn:parallelogram
 BEEAD  assumption 
  BEDAE  axiom:betweennesssymmetry
  CODAE  defn:collinear
  COADE  lemma:collinearorder
  NEAD  lemma:betweennotequal
  CODEF  lemma:collinear4
  CODFE  lemma:collinearorder
  EFDCBAFCBE proposition:35A
  EFDCBAEBCF axiom:EFpermutation
  EFEBCFDCBA axiom:EFsymmetric
  EFEBCFABCD axiom:EFpermutation
  EFABCDEBCF axiom:EFsymmetric
 NOBEEAD  reductio
 BEDAF  assumption
  ANBECHF+BEBHA  lemma:parallelPasch
  BECHF
  BEBHA
  BEAHB  axiom:betweennesssymmetry
  COCHF  defn:collinear
  COCFH  lemma:collinearorder
  NCDAC  lemma:parallelNC
  CODAF  defn:collinear
  EQAA  cn:equalityreflexive
  CODAA  defn:collinear
  NEAF lemma:betweennotequal
  NCAFC  lemma:NChelper
  NCCFA  lemma:NCorder
  ANBEAHB+COCFH+NCCFA
  OSACFB  defn:oppositeside
  OSBCFA  lemma:oppositesidesymmetric
  PREBCF  lemma:parallelflip
  PRCFEB   lemma:parallelsymmetric
  TPCFEB lemma:paralleldef2B
  SSEBCF  defn:tarski_parallel
  OSECFA lemma:planeseparation
  ANBEEeA+COCFe+NCCFE  defn:oppositeside
  BEEeA
  NEEA  lemma:betweennotequal
  NEeF  assumption
   COCFe
   CODAF
   CODAE  lemma:collinearorder
   NEDA   lemma:betweennotequal
   COAFE  lemma:collinear4
   COEAF  lemma:collinearorder
   COEeA  defn:collinear
   COEAe  lemma:collinearorder
   COAFe  lemma:collinear4 
   COeFA  lemma:collinearorder
   COeFC  lemma:collinearorder
   COFAC  lemma:collinear4
   COCFA   lemma:collinearorder
   NCCFA
  EQeF  reductio
  BEEFA  cn:equalitysub
  BEAFE  axiom:betweennesssymmetry
  BEDAF
  BEDAE  lemma:3.7b
  BEEAD  axiom:betweennesssymmetry
  NOBEEAD
 NOBEDAF reductio
 COADF
 OREQAD|EQAF|EQDF|BEDAF|BEADF|BEAFD defn:collinear
 COADE
 OREQAD|EQAE|EQDE|BEDAE|BEADE|BEAED  defn:collinear
 EQAF  assumption
  OREQFD|EQFE|EQDE|BEDAE|BEADE|BEAED  cn:equalitysub
  cases NEAF:EQFD|EQFE|EQDE|BEDAE|BEADE|BEAED
   case 1:EQFD
    EQAD cn:equalitysub
    EQAF assumption
     NEAD
    NEAF reductio
   qedcase
   case 2:EQFE
    EQAF assumption
     NEEF
     NEFE lemma:inequalitysymmetric
    NEAF reductio
   qedcase
   case 3:EQDE
    EQAF assumption
     ANBEEpC+BEBpF  lemma:diagonalsmeet
     BEEpC
     BEBpF
     COEpC  defn:collinear
     COBpF  defn:collinear
     COFBp  lemma:collinearorder
     COECp  lemma:collinearorder
     NCEFC  lemma:parallelNC
     NEEC   lemma:NCdistinct
     NCEFB  lemma:parallelNC
     NEFB   lemma:NCdistinct
     ANNEEC+NEFB+COECp+COFBp
     MEECFB defn:meet
     MEDCFB  cn:equalitysub
     MEDCAB  cn:equalitysub
     PRDCAB  lemma:parallelsymmetric
     NOMEDCAB  defn:parallel
    NEAF reductio
   qedcase
   case 4:BEDAE
    EQAF assumption
     BEEAD  axiom:betweennesssymmetry
     NOBEEAD
    NEAF reductio
   qedcase
   case 5:BEADE
    EQAF assumption
     NOBEADE
    NEAF reductio
   qedcase
   case 6:BEAED
    EQAF assumption
     EEAEAE  cn:congruencereflexive
     EEFEAE  cn:equalitysub
     EEAEFE  lemma:congruencesymmetric
     LTFEAD  defn:lessthan
     EEADEF
     LTFEEF lemma:lessthancongruence
     EEEFFE cn:equalityreverse
     LTFEFE  lemma:lessthancongruence
     NOLTFEFE  lemma:trichotomy2
    NEAF reductio
   qedcase
  NEAF cases
 NEAF  reductio
 EQDF  assumption
  OREQAF|EQAE|EQFE|BEDAE|BEADE|BEAED  cn:equalitysub
   cases NEDF:EQAF|EQAE|EQFE|BEDAE|BEADE|BEAED
    case 1:EQAF
     EQDF assumption
      NEAF
     NEDF reductio
    qedcase
    case 2:EQAE
     EQDF  assumption
      ANBEAMC+BEBMD  lemma:diagonalsmeet
      BEAMC
      BEBMD 
      COABC   assumption
       EQCC    cn:equalityreflexive
       COCDC   defn:collinear
       NEAB   defn:parallel
       NECD   defn:parallel
       MEABCD  defn:meet
       NOMEABCD  defn:parallel
      NCABC   reductio
      EFABCDABCD lemma:EFreflexive
      EFABCDEBCD  cn:equalitysub
      EFABCDEBCF  cn:equalitysub
     NEDF reductio
    qedcase
    case 3:EQFE
     EQDF assumption
      EQFE cn:equalitysub
      EQEF  lemma:equalitysymmetric
     NEDF reductio
    qedcase
    case 4:BEDAE
     EQDF assumption
      BEEAD axiom:betweennesssymmetry
      NOBEEAD
     NEDF reductio
    qedcase
    case 5:BEADE
     EQDF assumption
      NOBEADE
     NEDF reductio
    qedcase
    case 6:BEAED
     EQDF assumption
      BEDEA axiom:betweennesssymmetry
      EEDEDE  cn:congruencereflexive
      LTDEDA  defn:lessthan
      EEDEFE  cn:equalitysub
      LTFEDA  lemma:lessthancongruence2
      EEFEEF  cn:equalityreverse
      LTEFDA  lemma:lessthancongruence2
      EEDAAD  cn:equalityreverse
      LTEFAD  lemma:lessthancongruence
      EEADEF  
      LTEFEF  lemma:lessthancongruence
      NOLTEFEF  lemma:trichotomy2
     NEDF reductio
    qedcase
   NEDF cases
  NEDF reductio
 cases BEAFD:EQAD|EQAF|EQDF|BEDAF|BEADF|BEAFD
  case 1:EQAD
   NOBEAFD assumption
    NEAD
   BEAFD reductio
  qedcase
  case 2:EQAF
   NOBEAFD assumption
    NEAF
   BEAFD reductio
  qedcase
  case 3:EQDF
   NOBEAFD assumption
    NEDF
   BEAFD reductio
  qedcase
  case 4:BEDAF
   NOBEAFD assumption
    NOBEDAF
   BEAFD reductio
  qedcase
  case 5:BEADF
   NOBEAFD assumption
    NOBEADF
   BEAFD reductio
  qedcase
  case 6:BEAFD
   BEAFD
  qedcase
 BEAFD cases 
 cases BEAED:EQAD|EQAE|EQDE|BEDAE|BEADE|BEAED
  case 1:EQAD
   NOBEAED assumption
    NEAD  
   BEAED reductio
  qedcase
  case 2:EQAE
   NOBEAED assumption
    BEAFD
    EEAFAF cn:congruencereflexive
    EEAFEF  cn:equalitysub
    LTEFAD  defn:lessthan
    EEADEF 
    LTEFEF lemma:lessthancongruence
    NOLTEFEF lemma:trichotomy2
   BEAED reductio
  qedcase
  case 3:EQDE
   NOBEAED assumption
    BEDFA  axiom:betweennesssymmetry
    EEDFDF  cn:congruencereflexive
    LTDFDA  defn:lessthan
    LTEFDA  cn:equalitysub
    EEDAEF  lemma:congruenceflip
    LTEFEF  lemma:lessthancongruence
    NOLTEFEF lemma:trichotomy2
   BEAED reductio
  qedcase
  case 4:BEDAE
   NOBEAED assumption
    BEEAD axiom:betweennesssymmetry
    NOBEEAD
   BEAED reductio
  qedcase
  case 5:BEADE
   NOBEAED assumption
    NOBEADE
   BEAED reductio
  qedcase
  case 6:BEAED
   BEAED
  qedcase
 BEAED cases
 BEAEF assumption
  BEEFD  lemma:3.6a
  EEEFEF  cn:congruencereflexive
  LTEFED  defn:lessthan
  BEAED
  BEDEA  axiom:betweennesssymmetry
  EEDEDE cn:congruencereflexive
  LTDEDA defn:lessthan
  EEEDDE  cn:equalityreverse
  LTEFDE  lemma:lessthancongruence
  LTEFDA  lemma:lessthantransitive
  EEDAAD cn:equalityreverse
  LTEFAD lemma:lessthancongruence
  LTEFEF lemma:lessthancongruence
  NOLTEFEF lemma:trichotomy2
 NOBEAEF reductio
 BEAFE assumption
  BEFED lemma:3.6a
  EEFEFE  cn:congruencereflexive
  LTFEFD defn:lessthan
  BEAFD
  BEDFA  axiom:betweennesssymmetry
  EEDFDF cn:congruencereflexive
  LTDFDA defn:lessthan
  EEFDDF  cn:equalityreverse
  LTFEDF  lemma:lessthancongruence
  LTFEDA  lemma:lessthantransitive
  EEDAAD cn:equalityreverse
  LTFEAD lemma:lessthancongruence
  EEADFE  lemma:congruenceflip
  LTFEFE lemma:lessthancongruence
  NOLTFEFE lemma:trichotomy2
 NOBEAFE reductio
 EQEF  axiom:connectivity
 NEEF
EFABCDEBCF reductio