theorem Th1: :: TOPREAL2:1

for p1, p2 being Point of (TOP-REAL 2) st p1 <> p2 & p1 in R^2-unit_square & p2 in R^2-unit_square holds
ex P1, P2 being non empty Subset of (TOP-REAL 2) st
( P1 is_an_arc_of p1,p2 & P2 is_an_arc_of p1,p2 & R^2-unit_square = P1 \/ P2 & P1 /\ P2 = {p1,p2} )