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TGBAAEBE
BEAEC
ANBEBAH+EEAHAE+LTBEBH  defn:togethergreater
BEBAH
NEBA  lemma:betweennotequal
EEAHAE
LTBEBH
EQBE assumption
 LTBBBH cn:equalitysub
 ANBEBKH+EEBKBB  defn:lessthan
 BEBKH
 EEBKBB
 NEBK  assumption
  NEBB  axiom:nocollapse
  EQBB  cn:equalityreflexive
 EQBK   reductio
 BEBBH   cn:equalitysub
 NEBB  lemma:betweennotequal
 EQBB  cn:equalityreflexive
NEBE  reductio
NEAC  lemma:betweennotequal
ANBEBAF+EEAFAC  lemma:extension
BEBAF
EEAFAC
NEEC   lemma:betweennotequal
ANBEBEG+EEEGEC  lemma:extension
EEEGEC
EEACAF  lemma:congruencesymmetric
EEAEAH  lemma:congruencesymmetric
EEAEAE  cn:congruencereflexive
LTAEAC  defn:lessthan
LTAEAF  lemma:lessthancongruence
LTAHAF  lemma:lessthancongruence2
RAAHF defn:ray
BEAHF  lemma:lessthanbetween
EEECHF   lemma:differenceofparts
EEEGHF  lemma:congruencetransitive
LTBEBH
BEBEG
BEBAH
BEAHF
BEBHF  lemma:3.7a
LTBGBF   lemma:lessthanadditive
TGBAACBG defn:togethergreater
TTBAACBEEC  defn:togetherfour

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