let n be Element of NAT ; :: thesis: for A, B being non empty Subset of (TOP-REAL n) holds dist_min A,B >= 0
let A, B be non empty Subset of (TOP-REAL n); :: thesis: dist_min A,B >= 0
ex A9, B9 being Subset of (TopSpaceMetr (Euclid n)) st
( A = A9 & B = B9 & dist_min A,B = min_dist_min A9,B9 ) by Def1;
hence dist_min A,B >= 0 by Th11; :: thesis: verum