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REABCD
REPQEF
EEPQAB
EFABCDPQEF
ANRRDAB+RRABC+RRBCD+RRCDA+CRACBD  defn:rectangle
ANRRFPQ+RRPQE+RRQEF+RREFP+CRPEQF defn:rectangle
RRDAB   
RRABC  
RRPQE   
RRCDA   
CRACBD
NCDAB  lemma:rightangleNC
NCPQE  lemma:rightangleNC
NEAD  lemma:NCdistinct
NEAB  lemma:NCdistinct
NEQE  lemma:NCdistinct
RRBCD  defn:rectangle
NCBCD lemma:rightangleNC
NEBC  lemma:NCdistinct
NECD  lemma:NCdistinct
ANRABCe+EEBeQE  lemma:layoff
RABCe
EEBeQE
RRFPQ  defn:rectangle
NCFPQ  lemma:rightangleNC
NEPF  lemma:NCdistinct
ANRAADf+EEAfPF  lemma:layoff
RAADf
EEAfPF 
PGABCD   lemma:rectangleparallelogram
PRADBC   defn:parallelogram
COADf   lemma:rayimpliescollinear
COBCe  lemma:rayimpliescollinear
COCBe  lemma:collinearorder
PRBCAD  lemma:parallelsymmetric
EEPFAf  lemma:congruencesymmetric
NEAf   lemma:nullsegment3
NEfA  lemma:inequalitysymmetric
PRBCDA  lemma:parallelflip
CODAf  lemma:collinearorder
PRBCfA  lemma:collinearparallel
PRBCAf  lemma:parallelflip
PRAfBC  lemma:parallelsymmetric
EEQEBe  lemma:congruencesymmetric
NEBe  lemma:nullsegment3
NEeB  lemma:inequalitysymmetric
PRAfCB  lemma:parallelflip
PRAfeB  lemma:collinearparallel
PRfAeB  lemma:parallelflip
PRABCD  defn:parallelogram
TPABCD  lemma:paralleldef2B
SSCDAB  defn:tarski_parallel
EQAA   cn:equalityreflexive
COAAB   defn:collinear
SSCfAB  lemma:sameside2
SSfCAB  lemma:samesidesymmetric
EQBB  cn:equalityreflexive
COABB  defn:collinear
SSfeAB  lemma:sameside2
EEfAPF  lemma:congruenceflip
PGPQEF   lemma:rectangleparallelogram
EEPFQE  proposition:34
EEfAQE  lemma:congruencetransitive
EEQEBe  lemma:congruencesymmetric
EEQEeB  lemma:congruenceflip
EEfAeB  lemma:congruencetransitive
ANPRfAeB+EEfAeB+SSfeAB
ANPRfeAB+EEfeAB  proposition:33B
PRfeAB
EEfeAB
PRABfe  lemma:parallelsymmetric
PRABef  lemma:parallelflip
PRADBC  defn:parallelogram
PRADCB  lemma:parallelflip
COBCe  lemma:rayimpliescollinear
COCBe  lemma:collinearorder
PRADeB  lemma:collinearparallel
PRADBe  lemma:parallelflip
PRBeAD  lemma:parallelsymmetric
PRBeDA  lemma:parallelflip
COADf   lemma:rayimpliescollinear
CODAf  lemma:collinearorder
NEAf  lemma:raystrict
NEfA  lemma:inequalitysymmetric
PRBefA  lemma:collinearparallel
PRBeAf  lemma:parallelflip
PRAfBe  lemma:parallelsymmetric
PGABef  defn:parallelogram

TCBADDCB  proposition:34
TCBAffeB  proposition:34
EABAffeB  proposition:34
RAADf
RRBAD     lemma:8.2
RRBAf     lemma:8.3
EAfeBBAf  lemma:equalanglessymmetric
RRfeB     lemma:equaltorightisright
RABCe
RRABC     
RRABe     lemma:8.3
PGBefA    lemma:PGrotate
REBefA    lemma:PGrectangle
CRBfeA    defn:rectangle


ETBADDCB  axiom:congruentequal
ETBAffeB  axiom:congruentequal

ANBEAMC+BEBMD  defn:cross
BEAMC
BEBMD
ANBEBmf+BEemA  defn:cross
BEemA
BEAme  axiom:betweennesssymmetry
BEBmf
COBMD  defn:collinear
COBDM  lemma:collinearorder
NCBDA  lemma:NCorder
OSABDC  defn:oppositeside
COBmf   defn:collinear
COBfm  lemma:collinearorder
NCBAf  lemma:equalanglesNC
NCBfA  lemma:NCorder
OSABfe  defn:oppositeside
 
EEABAB  cn:congruencereflexive
EEPFAf  lemma:congruencesymmetric
RRFPQ
RRfAB   lemma:8.2
EAFPQfAB  lemma:Euclid4
TRFPQ  defn:triangle
NCfAB  lemma:parallelNC
TRfAB  defn:triangle
EEFQfB   proposition:04
EEFPfA  lemma:congruenceflip
TCFPQfAB  defn:trianglecongruence
ETFPQfAB  axiom:congruentequal
ETFPQfBA  axiom:ETpermutation
ETfBAFPQ  axiom:ETsymmetric
ETfBAFQP  axiom:ETpermutation
ETFQPfBA  axiom:ETsymmetric

EEQEBe  lemma:congruencesymmetric
PGPQEF
EEPQFE  proposition:34
EEPQEF  lemma:congruenceflip
EEABfe  proposition:34
EEEFPQ  lemma:congruencesymmetric
EEEFAB   lemma:congruencetransitive
EEEFfe  lemma:congruencetransitive
EEFEfe  lemma:congruenceflip
TCFQEfBe defn:trianglecongruence
ETFQEfBe  axiom:congruentequal
ANBEPpE+BEQpF  lemma:diagonalsmeet
BEPpE
BEQpF
COQpF  defn:collinear
COQFp  lemma:collinearorder
PRPQEF  defn:parallelogram
NCPQF   lemma:parallelNC
NCQFP   lemma:NCorder
OSPQFE   defn:oppositeside 
OSABfe    
OSAfBe   lemma:oppositesideflip
OSPFQE   lemma:oppositesideflip
EFFPQEfABe  axiom:paste3
EFFPQEABef  axiom:EFpermutation
EFABefFPQE  axiom:EFsymmetric
EFABefPQEF  axiom:EFpermutation
EFPQEFABef   axiom:EFsymmetric
EFABCDABef   axiom:EFtransitive
RAADf
COADf  lemma:rayimpliescollinear
COBCe  lemma:rayimpliescollinear
RRCDA
RRADC   lemma:8.2
RRDCB  lemma:8.2
CODAf  lemma:collinearorder
ORBEAfD|EQDf|BEADf  lemma:ray1
EEADBC proposition:34
EEAfBe proposition:34
NEfD assumption
 NEDf  lemma:inequalitysymmetric
 cases NECe:BEAfD|EQDf|BEADf
  case 1:BEAfD
   LTBeAD  defn:lessthan
   LTBeBC  lemma:lessthancongruence
   RABeC  lemma:ray5
   BEBeC   lemma:lessthanbetween
   EEfDeC lemma:differenceofparts
   NEeC  lemma:nullsegment3
   NECe  lemma:inequalitysymmetric
  qedcase
  case 2: EQDf
   EQCe assumption
    EQfD  lemma:equalitysymmetric
    NEfD
   NECe reductio
   qedcase
  case 3:BEADf
   EEBCAD  lemma:congruencesymmetric
   LTBCAf  defn:lessthan
   LTBCBe  lemma:lessthancongruence
   BEBCe  lemma:lessthanbetween
   EEDfCe  lemma:differenceofparts
   NECe  lemma:nullsegment3
  qedcase
 NECe cases  
 NEeC  lemma:inequalitysymmetric
 RRfDC lemma:collinearright
 COBCe  lemma:rayimpliescollinear
 RRBCD
 RReCD lemma:collinearright
 RRDCe  lemma:8.2
 PGABef
 PGBefA  lemma:PGrotate
 REBefA  lemma:PGrectangle
 RRefA  defn:rectangle  
 RRAfe lemma:8.2
 RRBef  defn:rectangle
 COADf  lemma:rayimpliescollinear
 COAfD  lemma:collinearorder
 RRDfe  lemma:collinearright
 RRefD  lemma:8.2
 COBCe  lemma:rayimpliescollinear
 COBeC  lemma:collinearorder
 RRCef  lemma:collinearright 
 BECMA  axiom:betweennesssymmetry
 BEfmB  axiom:betweennesssymmetry
 BEemA  axiom:betweennesssymmetry
 ORBEAfD|EQDf|BEADf  lemma:ray1
 cases CRDeCf:BEAfD|EQDf|BEADf
  case 1:BEAfD
   LTBeAD  defn:lessthan
   LTBeBC  lemma:lessthancongruence
   ANBEBhC+EEBhBe  defn:lessthan
   BEBhC
   EEBhBe
   NEBh  lemma:betweennotequal
   NEhB  lemma:inequalitysymmetric
   RABCh  lemma:ray4
   EQhe  lemma:layoffunique
   BEBeC  cn:equalitysub
   BEDMB axiom:betweennesssymmetry
   BECeB  axiom:betweennesssymmetry
   NCBCD  lemma:parallelNC
   NCDBC  lemma:NCorder
   ANBEDJe+BECJM  postulate:Pasch-inner
   BEDJe
   BECJM
   BECMA
   BECJA  lemma:3.6b
   BEDfA  axiom:betweennesssymmetry
   NCACD  lemma:parallelNC
   NCDAC  lemma:NCorder
   ANBEDKJ+BECKf  postulate:Pasch-inner
   BEDKJ
   BECKf
   BEDKe  lemma:3.6b
   ANBEDKe+BECKf
   CRDeCf  defn:cross
  qedcase
  case 2:EQDf
   NOCRDeCf  assumption
    NEDf 
   CRDeCf  reductio
  qedcase
  case 3:BEADf
   LTBCAf  defn:lessthan
   LTBCBe  lemma:lessthancongruence
   ANBEBge+EEBgBC  defn:lessthan
   BEBge
   EEBgBC
   RABeC  lemma:ray5
   NEge  lemma:betweennotequal
   NEeg  lemma:inequalitysymmetric
   NEBg lemma:betweennotequal
   RABge  lemma:ray4
   RABeg  lemma:ray5
   EQgC   lemma:layoffunique
   BEBCe  cn:equalitysub
   BEeCB  axiom:betweennesssymmetry
   PRABef defn:parallelogram
   NCBef  lemma:parallelNC
   NCfBe  lemma:NCorder
   BEfmB  axiom:betweennesssymmetry
   BEeCB  axiom:betweennesssymmetry
   ANBEfJC+BEeJm  postulate:Pasch-inner
   BEfJC
   BEeJm
   PRABef defn:parallelogram
   NCAef  lemma:parallelNC
   NCfAe  lemma:NCorder
   BEfDA  axiom:betweennesssymmetry
   BEeJm
   BEemA  axiom:betweennesssymmetry
   BEeJA  lemma:3.6b
   ANBEfKJ+BEeKD  postulate:Pasch-inner
   BEfKJ
   BEfJC
   BEfKC  lemma:3.6b
   BECKf  axiom:betweennesssymmetry
   BEeKD
   BEDKe  axiom:betweennesssymmetry
   CRDeCf defn:cross
  qedcase
 CRDeCf cases  
 ANRRfDC+RRDCe+RRCef+RRefD+CRDeCf
 REDCef  defn:rectangle
 PGDCef  lemma:rectangleparallelogram
 EEDfCe  proposition:34
 EEAfBe  proposition:34
 EEADBC  proposition:34 
 EEfDeC  lemma:congruenceflip
 cases EEADAf:BEAfD|EQDf|BEADf 
  case 1:BEAfD
   NOEEADAf  assumption   
    BEBeC  lemma:betweennesspreserved
    REfeCD lemma:rectanglereverse 
    NOEFABefABCD  axiom:deZolt2
    EFABCDABef
    EFABefABCD  axiom:EFsymmetric
   EEADAf reductio
  qedcase
  case 2:EQDf
   EEAfAf  cn:congruencereflexive
   EEADAf  cn:equalitysub
  qedcase
  case 3:BEADf
   NOEEADAf assumption
    BEBCe  lemma:betweennesspreserved
    NOEFABCDABef  axiom:deZolt2
   EEADAf reductio
  qedcase
 EEADAf cases
 EQDD cn:equalityreflexive
 RAADD lemma:ray4
 EEAfAD  lemma:congruencesymmetric
 EQfD lemma:layoffunique
EQfD reductio
EEADPF  cn:equalitysub