for P1, P2 being Subset of (TOP-REAL 2)
for p1, p2, q1, q2 being Point of (TOP-REAL 2) st P1 is_S-P_arc_joining p1,q1 & P2 is_S-P_arc_joining p2,q2 & ( for p being Point of (TOP-REAL 2) st p in P1 \/ P2 holds
( p1 `1 <= p `1 & p `1 <= q1 `1 ) ) & ( for p being Point of (TOP-REAL 2) st p in P1 \/ P2 holds
( p2 `2 <= p `2 & p `2 <= q2 `2 ) ) holds
P1 meets P2