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TGAaBbCc
ANBEAaH+EEaHBb+LTCcAH  defn:togethergreater
BEAaH 
EEaHBb
LTCcAH
NEAa   lemma:betweennotequal
NEaA   lemma:inequalitysymmetric
NEaH   lemma:betweennotequal
NEBb   axiom:nocollapse
ANBEaAh+EEAhBb   lemma:extension
EEAaaA   cn:equalityreverse
EEaHBb
EEAhBb
EEBbAh  lemma:congruencesymmetric
EEaHAh  lemma:congruencetransitive
BEAaH
BEaAh
EEAHah  cn:sumofparts
LTCcah  lemma:lessthancongruence
TGaABbCc defn:togethergreater
EECccC   cn:equalityreverse
LTcCAH   lemma:lessthancongruence2
TGAaBbcC  defn:togethergreater
ANTGaABbCc+TGAaBbcC

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