theorem Th23: :: GTARSKI5:23

for S being non empty satisfying_Tarski-model satisfying_Lower_Dimension_Axiom TarskiGeometryStruct
for a, b being POINT of S
for A being Subset of S st A is_line & not a in A & not b in A & b in half-plane (A,a) holds
half-plane (A,b) = half-plane (A,a)