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LTABCD
BEABE
BECDF
EEBEDF
ANBECbD+EECbAB   defn:lessthan
BECbD
EECbAB
EEABCb   lemma:congruencesymmetric
NECb  lemma:betweennotequal
NEBE  lemma:betweennotequal
ANBECbe+EEbeBE  lemma:extension
EEbeBE
EEBEbe  lemma:congruencesymmetric
BECDF
BECbD
BECbF  lemma:3.6b
BEbFe  assumption
 EEFDFD  cn:congruencereflexive
 BECbD
 BECDF
 BEbDF  lemma:3.6a
 BEFDb   axiom:betweennesssymmetry
 LTFDFb   defn:lessthan
 EEFbbF   cn:equalityreverse
 LTFDbF   lemma:lessthancongruence
 EEFDDF   cn:equalityreverse
 LTDFbF  lemma:lessthancongruence2
 EEbeBE
 EEBEDF
 EEbeDF  lemma:congruencetransitive
 EEDFbe  lemma:congruencesymmetric
 LTbebF  lemma:lessthancongruence2
 ANBEbqF+EEbqbe  defn:lessthan
 BEbqF
 EEbqbe
 NEbF  lemma:betweennotequal
 RAbFq  lemma:ray4
 RAbFe  lemma:ray4
 EQqe   lemma:layoffunique
 BEbeF  cn:equalitysub
 BEFeF  lemma:3.6a
 NOBEFeF  axiom:betweennessidentity
NOBEbFe  reductio
EQFe   assumption
 EEbeBE
 EEbFBE  cn:equalitysub
 BECbD
 BECDF
 BEbDF  lemma:3.6a
 BEFDb  axiom:betweennesssymmetry
 EEFDFD  cn:congruencereflexive
 LTFDFb  defn:lessthan
 EEFbbF  cn:equalityreverse
 LTFDbF  lemma:lessthancongruence
 EEDFBE  lemma:congruencesymmetric
 EEFDBE  lemma:congruenceflip
 LTBEbF  lemma:lessthancongruence2
 EEbFbe  lemma:congruencetransitive
 LTBEbe  lemma:lessthancongruence
 EEbeBE
 LTBEBE  lemma:lessthancongruence
 NOLTBEBE lemma:trichotomy2
NEFe  reductio
BECbe
BECbF
NOBEbeF  assumption
 NOBEbFe
 EQFe   lemma:outerconnectivity
 NEFe 
BEbeF  reductio
BECbe
BECeF  lemma:3.7a
EEABCb
EEBEbe
EEAECe  cn:sumofparts
EECeAE  lemma:congruencesymmetric
LTAECF  defn:lessthan