theorem :: EUCLID_4:44

for n being Nat
for p1, p2 being Point of (TOP-REAL n)
for A, C being Subset of (TOP-REAL n) st A is being_line & C is being_line & p1 in A & p2 in A & p1 in C & p2 in C & not p1 = p2 holds
A = C