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TRABC
RRBAC
SQBCED
OSDCBA
ANBEDNA+COCBN+NCCBD  defn:oppositeside
BEDNA
COCBN
RRCAB  lemma:8.2
NCCAB lemma:rightangleNC
NEAB  lemma:NCdistinct
NCABC  defn:triangle
NEBC  lemma:NCdistinct
EEBCED  defn:square
NEED  axiom:nocollapse
NEDE  lemma:inequalitysymmetric
OSDCBA
ANBEDqA+COCBq+NCCBD  defn:oppositeside
BEDqA
COCBq
NCCBD   
PGBCED lemma:squareparallelogram
PRBCED defn:parallelogram
NOMEBCED defn:parallel
EQAE assumption
 BEDqE  cn:equalitysub
 CODqE  defn:collinear
 COEDq  lemma:collinearorder
 COBCq  lemma:collinearorder
 MEBCED defn:meet
NEAE reductio
CODEA assumption
 CODAE  lemma:collinearorder
 CODqA  defn:collinear
 CODAq  lemma:collinearorder
 NEDA  lemma:betweennotequal
 COAEq  lemma:collinear4
 COqAE lemma:collinearorder
 COqAD lemma:collinearorder
 NEqA  lemma:betweennotequal
 COAED lemma:collinear4
 COAEq lemma:collinearorder
 COEDq  lemma:collinear4
 COBCq  lemma:collinearorder
 MEBCED  defn:meet
NCDEA reductio
% Now drop perpendicular AL to DE from A
% Euclid draws AL parallel to BD but then why would it meet DE?
PAALDEL   proposition:12
ANCOALL+CODEL+CODEp+RRpLA  defn:perpat
CODEL
CODEp
RRpLA
RRALp  lemma:8.2
EQBN  assumption
 BEDBA  cn:equalitysub
 CODBA  defn:collinear
 RRDBC  defn:square
 RRABC  lemma:collinearright
 NORRCAB  lemma:8.7
 RRCAB  lemma:8.2  
NEBN  reductio
PGBCED
PRBCED  defn:parallelogram
PRBCDE  lemma:parallelflip
PRDEBC  lemma:parallelsymmetric
PRDECB  lemma:parallelflip
NENB  lemma:inequalitysymmetric
PRDENB  lemma:collinearparallel
PRDEBN  lemma:parallelflip
TPDEBN  lemma:paralleldef2B
SSBNDE  defn:tarski_parallel
EQDD   cn:equalityreflexive
CODDE  defn:collinear
NEDN   lemma:betweennotequal
RADNA   lemma:ray4
SSBADE  lemma:sameside2
SSBAED  lemma:samesideflip
SSABED  lemma:samesidesymmetric 
EQDL  assumption
 RRADp  cn:equalitysub
 RRpDA  lemma:8.2
 COpDE lemma:collinearorder
 RREDA  lemma:collinearright
 RREDB  defn:square
 SSABED 
 RADAB  lemma:erectedperpendicularunique
 CODAB  lemma:rayimpliescollinear
 COADB  lemma:collinearorder
 CODNA  defn:collinear
 COADN  lemma:collinearorder
 NEDA  lemma:betweennotequal
 NEAD  lemma:inequalitysymmetric
 CODBN lemma:collinear4
 CONBC  lemma:collinearorder
 CONBD  lemma:collinearorder
 COBCD  lemma:collinear4
 NCBCD  lemma:NCorder
NEDL  reductio
NELD  lemma:inequalitysymmetric
PRBCED  lemma:parallelflip
COEDL  lemma:collinearorder
PRBCLD  lemma:collinearparallel
PRLDBC  lemma:parallelsymmetric
TPBCLD  lemma:paralleldef2B
SSLDBC  defn:tarski_parallel
NCBCD   lemma:parallelNC
COBCN lemma:collinearorder
OSDBCA  defn:oppositeside
OSLBCA  lemma:planeseparation
ANBELMA+COBCM+NCBCL  defn:oppositeside
BELMA
COBCM
NEDE  lemma:NCdistinct
NEED  lemma:inequalitysymmetric
NELM  lemma:betweennotequal
RALMA lemma:ray4
RALAM  lemma:ray5
RREDB  defn:square
RRpLA
CODEp
COEDp lemma:collinearorder
COEDL lemma:collinearorder
CODpL  lemma:collinear4
COpLD  lemma:collinearorder
RRDLA  lemma:collinearright
RRDLM  lemma:8.3
EQBM  assumption
 RRDLB  cn:equalitysub
 RRLDB  lemma:collinearright
 RRBDL  lemma:8.2
 NORRBDL  lemma:8.7
NEBM  reductio
NEMB  lemma:inequalitysymmetric
PRLDCB  lemma:parallelflip
COCBM   lemma:collinearorder
PRLDMB  lemma:collinearparallel
PRLDBM  lemma:parallelflip
PRBMLD  lemma:parallelsymmetric
PRBMDL  lemma:parallelflip
PRDLBM  lemma:parallelsymmetric
TPDLBM  lemma:paralleldef2B
SSBMDL   defn:tarski_parallel
PRBMLD  lemma:parallelsymmetric
RRLDB  lemma:collinearright
RRBDL  lemma:8.2
PRBDLM lemma:twoperpsparallel
PRBDML  lemma:parallelflip
PGBMLD  defn:parallelogram
PRMLBD  lemma:parallelsymmetric
TPMLBD  lemma:paralleldef2B
SSBDML  defn:tarski_parallel
BEAML  axiom:betweennesssymmetry
PRMBLD lemma:parallelflip
EAAMBMLD  proposition:29C
RRMLD   lemma:8.2
RRAMB  lemma:equaltorightisright
EQBB  cn:equalityreflexive
COBCB  defn:collinear
BEBMC   lemma:altitudeofrighttriangle
EQMC assumption
 RRAMB
 RRACB cn:equalitysub
 NORRBAC lemma:8.7
NEMC reductio
EQLE  assumption
 PGBCED
 PRBDCE  defn:parallelogram
 PRCEBD  lemma:parallelsymmetric
 PRMEBD  cn:equalitysub
 PRBDME  lemma:parallelsymmetric
 PRBDCE  lemma:parallelsymmetric
 PRBDEC  lemma:parallelflip
 PRBDEM  lemma:parallelflip
 COECM   lemma:Playfair
 COMCE   lemma:collinearorder
 COMCB  lemma:collinearorder
 NEMC 
 COCEB  lemma:collinear4
 COBCE  lemma:collinearorder
 NCBCE  lemma:parallelNC
NELE reductio
PRBMLD  defn:parallelogram
PRBMDL  lemma:parallelflip
CODLE   lemma:collinearorder
NEEL  lemma:inequalitysymmetric
PRBMEL lemma:collinearparallel
PRELBM lemma:parallelsymmetric
COBMC  lemma:collinearorder
NECM   lemma:inequalitysymmetric
PRELCM  lemma:collinearparallel
PRCMEL  lemma:parallelsymmetric
PRMCEL  lemma:parallelflip
RRDLM
CODLE  lemma:collinearorder
RRELM  lemma:collinearright
RRMLE  lemma:8.2
RRCED   defn:square
RRDEC   lemma:8.2
CODEL
NELE
RRLEC  lemma:collinearright
PRMCLE lemma:parallelflip
PRLEMC  lemma:parallelsymmetric
TPLEMC  lemma:paralleldef2B
SSMCLE  defn:tarski_parallel
PRMLEC  lemma:twoperpsparallel
PRMLCE  lemma:parallelflip
PGMCEL  defn:parallelogram
EEBMDL   proposition:34
EEMCLE   proposition:34
EEBCDE   proposition:34
BEBMC
BEDLE    lemma:betweennesspreserved
ANPGBMLD+BEBMC+PGMCEL+BEDLE+BELMA+RRDLA