Sindbad~EG File Manager

NCJEN
NCABD
NCCBD
BEAOC
BEBOD
NERK
NCKRS
NEBD  lemma:NCdistinct
ANBEBmD+EEmBmD  proposition:10
BEBmD
EEmBmD
EEBmmD  lemma:congruenceflip
MIBmD  defn:midpoint
NEBm  lemma:betweennotequal
ANBERKP+EEKPBm lemma:extension
BERKP
EEKPBm
% set up for 42B
TRABD  defn:triangle
MIBmD
NCJEN
NEKP lemma:betweennotequal
NEPK  lemma:inequalitysymmetric
ANBEPKH+EEKHPK  lemma:extension
BEPKH
EEKHPK
EEPKKH lemma:congruencesymmetric
MIPKH  defn:midpoint

% KH = PK = Bm = mD
EEPKBm  lemma:congruenceflip
EEKHBm  lemma:congruencetransitive
EEBmmD  lemma:congruenceflip
EEKHmD  lemma:congruencetransitive
BEPKR  axiom:betweennesssymmetry
COPKH  defn:collinear
COPKR  defn:collinear
NEPK  lemma:betweennotequal
COKHR  lemma:collinear4
CORKH  lemma:collinearorder
NCRKS  lemma:NCorder
EQKK  cn:equalityreflexive
CORKK  defn:collinear
NEKH  lemma:betweennotequal
NEHK  lemma:inequalitysymmetric
NCHKS   lemma:NChelper
NCSKH  lemma:NCorder
ANPGFKHG+EFABmDFKHG+EAHKFJEN+SSSFKH proposition:42B
PGFKHG

%Now set up to apply 44

NCDBC  lemma:NCorder
TRDBC  defn:triangle
PRFKHG  defn:parallelogram
NCKHG  lemma:parallelNC
NCHGK  lemma:NCorder
NCGHK  lemma:NCorder
ANPGGHML+EAGHMJEN+EFDBeCGHML+MIBeC+OSMGHK proposition:44
EAGHMJEN
MIBeC
BEBeC  defn:midpoint
PGFKHG
PGGHML
EAHKFJEN
EAJENGHM  lemma:equalanglessymmetric
EAHKFGHM  lemma:equalanglestransitive
PRFKHG  defn:parallelogram
PRKFHG  lemma:parallelflip
NEHK lemma:NCdistinct
ANBEHKs+EEKsHK lemma:extension
PRFGKH  defn:parallelogram
PRKHFG  lemma:parallelsymmetric
TPKHFG  lemma:paralleldef2B
SSFGKH  defn:tarski_parallel
RTFKHKHG   proposition:29C
EAGHMHKF  lemma:equalanglessymmetric
NCHKF  lemma:equalanglesNC
NCFKH  lemma:NCorder
EAFKHHKF  lemma:ABCequalsCBA
EAFKHGHM  lemma:equalanglestransitive
RTGHMKHG  lemma:RTcongruence
RTKHGGHM  lemma:RTsymmetric

%Next to show BEKHM

OSMGHK 
EQGG  cn:equalityreflexive
NEHG  lemma:NCdistinct
RAHGG  lemma:ray4
RTKHGGHM 
BEKHM   proposition:14

%next to show PRFKLM  using I.30

NEFK  lemma:NCdistinct
NCGHM  lemma:equalanglesNC
NEGH  lemma:NCdistinct
PRGHML  defn:parallelogram
NCHML  lemma:parallelNC
NELM  lemma:NCdistinct
EQKK  cn:equalityreflexive
EQHH  cn:equalityreflexive
EQMM  cn:equalityreflexive
COFKK  defn:collinear
COGHH  defn:collinear
COLMM  defn:collinear
BEKHM
PRFKGH  lemma:parallelflip
PRMLGH  lemma:parallelsymmetric
PRLMGH   lemma:parallelflip
PRFKLM  proposition:30
PRFKML  lemma:parallelflip

% Next show FG and LF both parallel KM and apply Playfair
% Euclid essentially gives a proof of Playfair here instead

PGFKHG
PGGHML
PRFGKH  defn:parallelogram
PRGLHM  defn:parallelogram
PRFGHK  lemma:parallelflip
COKHM  defn:collinear
COHKM  lemma:collinearorder
NEKM  lemma:betweennotequal
NEMK  lemma:inequalitysymmetric
PRFGMK  lemma:collinearparallel
COHMK  lemma:collinearorder
PRGLKM  lemma:collinearparallel
PRGLMK  lemma:parallelflip
PRMKGL  lemma:parallelsymmetric
PRMKFG  lemma:parallelsymmetric
PRMKGF  lemma:parallelflip
COGLF   lemma:Playfair
COGFL   lemma:collinearorder
NCFLM  lemma:parallelNC
NELF   lemma:NCdistinct
PRMKLF  lemma:collinearparallel
PRLFMK  lemma:parallelsymmetric
PRFLKM  lemma:parallelflip
PGFKML  defn:parallelogram
EAHKFJEN
NCFKH  lemma:parallelNC
EAFKHHKF  lemma:ABCequalsCBA
EAFKHJEN  lemma:equalanglestransitive
NEKH  lemma:betweennotequal
RAKHM  lemma:ray4
RAKMH  lemma:ray5
EQFF  cn:equalityreflexive
NEKF lemma:NCdistinct
RAKFF  lemma:ray4
NCFKM  lemma:parallelNC
EAFKMFKM  lemma:equalanglesreflexive
EAFKMFKH  lemma:equalangleshelper
EAFKMJEN  lemma:equalanglestransitive
EFABmDFKHG
EFDBeCGHML
COBOD  defn:collinear
COBDO  lemma:collinearorder
NCBDA  lemma:NCorder
OSABDC  defn:oppositeside
BEKHM
% Next prove BEFGL
PRGHLM lemma:parallelflip
TPGHLM  lemma:paralleldef2B
SSLMGH  defn:tarski_parallel
PRFKGH lemma:parallelflip
PRGHFK  lemma:parallelsymmetric
TPGHFK  lemma:paralleldef2B
SSFKGH  defn:tarski_parallel
EQHH   cn:equalityreflexive
COGHH  defn:collinear
OSKGHM  defn:oppositeside
OSFGHM  lemma:planeseparation
OSMGHF  lemma:oppositesidesymmetric
OSLGHF  lemma:planeseparation
ANBELtF+COGHt+NCGHL  defn:oppositeside
BELtF
COGHt
COFLG lemma:collinearorder
COLtF  defn:collinear
COFLt  lemma:collinearorder
NEFL  lemma:NCdistinct
COLGt lemma:collinear4
COtGL  lemma:collinearorder
COtGH  lemma:collinearorder
NEtG  assumption
 COGLH   lemma:collinear4
 COGHL   lemma:collinearorder
 NCGHL
EQtG  reductio
BELGF  cn:equalitysub
BEFGL  axiom:betweennesssymmetry
PGFKML
ANBEFjM+BEKjL  lemma:diagonalsmeet
BEFjM
BEKjL 
EFABCDFKML  axiom:paste4
EFFKMLABCD   axiom:EFsymmetric 
BEPKH
BEKHM  
BEPKR
BEPKM  lemma:3.7b
ANBEPKM+BEPKR
RAKRM  defn:ray
SSSFKH 
SSFSKH  lemma:samesidesymmetric
COKHM defn:collinear
SSFSKM lemma:samesidecollinear
ANPGFKML+EAFKMJEN+EFFKMLABCD+RAKRM+SSFSKM