Sindbad~EG File Manager

TRABC
NCJDK
MIBEC
ANBEBEC+EEBEEC  defn:midpoint
BEBEC
EEBEEC
EEEBEC  lemma:congruenceflip
NCABC  defn:triangle
COBEC  defn:collinear
NCBCA  lemma:NCorder
COBCE  lemma:collinearorder
EQCC  cn:equalityreflexive
COBCC  defn:collinear
NEEC lemma:betweennotequal
NCECA lemma:NChelper
ANRAECc+EAfEcJDK+SSfAEC proposition:23C
SSfAEC
NCBCA lemma:NCorder
ANBEPAQ+EAQAEAEB+EAQAEBEA+EAEAQBEA+EAPAEAEC+EAPAECEA+EAEAPCEA+PRPQBC+EEPAEC+EEAQBE+EEAMME+EEPMMC+EEBMMQ+BEPMC+BEBMQ+BEAME  proposition:31
BEPAQ
EAPAEAEC
BEPMC
BEAME 
EEPMMC
EEAMME
EEBMMQ
EAAECPAE  lemma:equalanglessymmetric
NCPAE  lemma:equalanglesNC
NCEAP  lemma:NCorder
SSAfEC  lemma:samesidesymmetric
NCBCA   lemma:NCorder
COBCE  lemma:collinearorder
EQBB  cn:equalityreflexive
EQAA   cn:equalityreflexive
COBCB defn:collinear
NEBE lemma:betweennotequal
NCBEA  lemma:NChelper
EQCC  cn:equalityreflexive
COBCC  defn:collinear
NEEC  lemma:betweennotequal
NECE lemma:inequalitysymmetric
NCCEA  lemma:NChelper
NEEA lemma:NCdistinct
%Now show Ef has to meet PQ, which Euclid fails to mention
NOMEEfPQ assumption
 AOCEfCEA  assumption
  RAECC  lemma:ray4
  RAEAA  lemma:ray4
  ANBEAmC+RAEfm  lemma:crossbar2
  BEAmC
  RAEfm
  BECmA  axiom:betweennesssymmetry
  BECMP  axiom:betweennesssymmetry
  BEEMA  axiom:betweennesssymmetry
  EEMEAM  lemma:congruencesymmetric
  EEEMAM  lemma:congruenceflip
  EEMCPM lemma:congruencesymmetric
  EEMCMP  lemma:congruenceflip
  ANBEEmF+BEPAF postulate:Euclid5
  BEEmF
  BEPAF 
  COEmF  defn:collinear
  COmEF  lemma:collinearorder
  COEfm  lemma:rayimpliescollinear
  COmEf  lemma:collinearorder
  NEEm  lemma:betweennotequal
  NEmE  lemma:inequalitysymmetric
  COEfF lemma:collinear4
  COPAF  defn:collinear
  COPAQ  defn:collinear
  NEPA  lemma:betweennotequal
  NEAP lemma:inequalitysymmetric
  COAPF lemma:collinearorder
  COAPQ lemma:collinearorder
  COPFQ lemma:collinear4
  COPQF lemma:collinearorder
  NEEf  lemma:ray2
  NEPQ lemma:betweennotequal
  MEEfPQ  defn:meet
 NOAOCEfCEA reductio
 COECB  lemma:collinearorder
 NEBE  lemma:betweennotequal
 NEEB  lemma:inequalitysymmetric
 SSAfEB  lemma:samesidecollinear
 SSfAEB  lemma:samesidesymmetric
 BECEB   axiom:betweennesssymmetry
 EQAA   cn:equalityreflexive
 EQff   cn:equalityreflexive
 NCEBf  defn:sameside
 NEEf  lemma:NCdistinct
 COBEC  defn:collinear
 COEBC  lemma:collinearorder
 EQEE  cn:equalityreflexive
 COEBE  defn:collinear 
 NCECf  lemma:NChelper
 NCCEf  lemma:NCorder 

 AOCEACEf  assumption
  RAEAA  lemma:ray4
  RAEff  lemma:ray4
  SUCEAAB  defn:supplement
  SUCEffB  defn:supplement
  AOfEBAEB  lemma:supplementinequality
  NCBEf  lemma:NCorder
  EABEffEB  lemma:ABCequalsCBA
  AOBEfAEB  lemma:angleorderrespectscongruence2
  EABEAAEB  lemma:ABCequalsCBA
  AOBEfBEA  lemma:angleorderrespectscongruence
  RAEBB  lemma:ray4
  RAEAA  lemma:ray4
  ANBEAmB+RAEfm lemma:crossbar2 
  BEAmB
  RAEfm
  BEBmA  axiom:betweennesssymmetry
  BEBMQ  
  BEEMA  axiom:betweennesssymmetry
  EEMEAM  lemma:congruencesymmetric
  EEEMAM  lemma:congruenceflip
  EEMBMQ  lemma:congruenceflip
  NCEAP 
  NCPAE  lemma:NCorder
  COPAQ  defn:collinear
  EQAA  cn:equalityreflexive
  COPAA  defn:collinear
  NEAQ  lemma:betweennotequal
  NEQA  lemma:inequalitysymmetric
  NCQAE lemma:NChelper
  NCEAQ  lemma:NCorder
  ANBEEmF+BEQAF postulate:Euclid5
  BEEmF
  BEQAF 
  COEmF  defn:collinear
  COmEF  lemma:collinearorder
  COEfm  lemma:rayimpliescollinear
  COmEf  lemma:collinearorder
  NEEm  lemma:betweennotequal
  NEmE  lemma:inequalitysymmetric
  COEfF lemma:collinear4
  COQAF  defn:collinear
  BEQAP  axiom:betweennesssymmetry
  COQAP  defn:collinear
  NEQA  lemma:betweennotequal
  NEAQ lemma:inequalitysymmetric
  COAQF lemma:collinearorder
  COAQP lemma:collinearorder
  COQFP lemma:collinear4
  COPQF lemma:collinearorder
  NEEf  lemma:ray2
  NEQP lemma:betweennotequal
  NEPQ  lemma:inequalitysymmetric
  MEEfPQ  defn:meet 
 NOAOCEACEf reductio
 NOEACEACEf  assumption
  NCCEA 
  NCCEf
  AOCEACEf  lemma:angletrichotomy2
 EACEACEf  reductio
 % We will show RAEfA so Ef meets PQ in A 
 ANRAECd+RAEAa+RAECp+RAEfq+EEEdEp+EEEaEq+EEdapq+NCCEA defn:equalangles 
 RAEAa
 RAEfq
 RAECp
 RAECd
 EEEdEp
 EEEaEq
 EEdapq
 COPQA  defn:collinear
 EQdp  lemma:layoffunique
 EEdadq cn:equalitysub
 EEadqd lemma:congruenceflip
 EEaEqE lemma:congruenceflip
 NEEd  lemma:raystrict
 SSAfEC
 COECd  lemma:rayimpliescollinear
 SSAfEd lemma:samesidecollinear
 COEdE  defn:collinear
 COEEd  lemma:collinearorder
 SSAqEd  lemma:sameside2
 SSqAEd lemma:samesidesymmetric
 SSqaEd  lemma:sameside2
 SSaqEd  lemma:samesidesymmetric
 EQaq   proposition:07
 COEAa  lemma:rayimpliescollinear
 COEfq  lemma:rayimpliescollinear
 COEAq  cn:equalitysub
 COqEA  lemma:collinearorder
 COqEf  lemma:collinearorder
 NEEq lemma:raystrict
 NEqE  lemma:inequalitysymmetric
 COEAf  lemma:collinear4
 COEfA  lemma:collinearorder
 NEPQ   lemma:betweennotequal
 MEEfPQ  defn:meet 
MEEfPQ  reductio
ANNEEf+NEPQ+COEfF+COPQF  defn:meet
NEPQ
PRPQBC
COBCE
NECE  lemma:inequalitysymmetric
PRPQEC  lemma:collinearparallel
PRECPQ   lemma:parallelsymmetric
COPQF
ANPGFGCE+COPQG lemma:triangletoparallelogram
PGFGCE
PGGFEC  lemma:PGflip
PGFECG  lemma:PGrotate
COPQF
COPQG
COPAQ   defn:collinear
COPQA   lemma:collinearorder
PRFECG  defn:parallelogram
NCFEG  lemma:parallelNC
NEFG   lemma:NCdistinct
COFGA  lemma:collinear5
ETFECAEC   proposition:41
PRPQCB   lemma:parallelflip
COCBE   lemma:collinearorder
NEEB     lemma:inequalitysymmetric
PRPQEB   lemma:collinearparallel
PRPQBE   lemma:parallelflip
COPQA
EEBEEC   lemma:congruenceflip
COBEC
EQEE     cn:equalityreflexive
COBEE    defn:collinear
ETABEAEC   proposition:38
ETAECABE   axiom:ETsymmetric
ETAECAEB   axiom:ETpermutation
ETAEBAEC   axiom:ETsymmetric
EQEE    cn:equalityreflexive
COAEE  defn:collinear
NCAEB     lemma:NCorder
OSBAEC    defn:oppositeside
PGFECG
PGEFGC   lemma:PGflip
TCFECCGF   proposition:34
ETFECCGF   axiom:congruentequal
ETFECFCG   axiom:ETpermutation
ETFCGFEC   axiom:ETsymmetric
ETFCGFCE   axiom:ETpermutation
ETFCEFCG   axiom:ETsymmetric
ANBEEmG+BEFmC  lemma:diagonalsmeet
BEEmG
BEFmC
COFmC  defn:collinear
COFCm  lemma:collinearorder
PRFECG   defn:parallelogram
NCFEC   lemma:parallelNC
NCFCE   lemma:NCorder
OSEFCG     defn:oppositeside
ETFCEFCG
ETAEBAEC 
ETFECAEC
ETAECFEC  axiom:ETsymmetric
ETAEBFEC  axiom:ETtransitive
ETAEBFCE  axiom:ETpermutation
ETAECFEC  axiom:ETsymmetric
ETFCGFCE  axiom:ETsymmetric
ETFCGFEC  axiom:ETpermutation
ETFECFCG  axiom:ETsymmetric
ETAECFCG axiom:ETtransitive 
EFABECFECG  axiom:paste3
RAECc   
NCFEC  lemma:parallelNC
NCCEF  lemma:NCorder
EACEFCEF   lemma:equalanglesreflexive
COEfF
SSfAEC
OREQEf|EQEF|EQfF|BEfEF|BEEfF|BEEFf  defn:collinear
NEFE lemma:NCdistinct
NEEF lemma:inequalitysymmetric
cases RAEFf:EQEf|EQEF|EQfF|BEfEF|BEEfF|BEEFf
 case 1:EQEf
  NORAEFf assumption
   NEEf
  RAEFf reductio
 qedcase
 case 2:EQEF
  NORAEFf assumption
   NEEF
  RAEFf reductio
 qedcase
 case 3:EQfF
  EQFF  cn:equalityreflexive
  NEEF
  RAEFF lemma:ray4
  RAEFf  cn:equalitysub
 qedcase
 case 4:BEfEF
  NORAEFf assumption
   EQEE  cn:equalityreflexive
   COECE defn:collinear
   BEFEf  axiom:betweennesssymmetry
   NCECF   lemma:NCorder
   OSFECf  defn:oppositeside
   OSfECF  lemma:oppositesidesymmetric
   SSAfEC  lemma:samesidesymmetric
   OSAECF  lemma:planeseparation
   ANBEAjF+COECj+NCECA  defn:oppositeside
   BEAjF
   COECj
   COAjF  defn:collinear
   COPQA
   COPQF
   NEPQ  lemma:betweennotequal
   NEQP lemma:inequalitysymmetric
   COQAF  lemma:collinear4
   COAFQ  lemma:collinearorder
   COQPA lemma:collinearorder
   COQPF lemma:collinearorder
   COPAF lemma:collinear4
   COAFP  lemma:collinearorder
   COAFj  lemma:collinearorder
   NEPQ  lemma:betweennotequal
   NEAF  lemma:betweennotequal
   COPQj  lemma:collinear5
   MEPQEC  defn:meet
   PRPQEC
   NOMEPQEC  defn:parallel
  RAEFf reductio
 qedcase
 case 5:BEEfF
  RAEFf  lemma:ray4
 qedcase
 case 6:BEEFf
  RAEFf  lemma:ray4
 qedcase
RAEFf cases
EACEFcEf   lemma:equalangleshelper
EAFECfEc  lemma:equalanglesflip
EAfEcJDK
EAFECJDK  lemma:equalanglestransitive
EACEFFEC  lemma:ABCequalsCBA
EACEFJDK  lemma:equalanglestransitive
ANPGFECG+EFABECFECG+EACEFJDK+COFGA