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ORBEAEB|EQEB|BEABE NEAB EQBA assumption EQAB lemma:equalitysymmetric NEBA reductio ANBEBAJ+EEAJAB lemma:extension BEBAJ BEJAB axiom:betweennesssymmetry cases RAABE:BEAEB|EQEB|BEABE case 1: BEAEB BEJAB BEJAE axiom:innertransitivity RAABE defn:ray qedcase case 2: EQEB BEJAB BEJAE cn:equalitysub RAABE defn:ray qedcase case 3: BEABE BEJAB BEJAE lemma:3.7b RAABE defn:ray qedcase RAABE cases