let n be Element of NAT ; :: thesis: for r being real number
for x being Point of (TOP-REAL n) holds Ball x,r c= cl_Ball x,r
let r be real number ; :: thesis: for x being Point of (TOP-REAL n) holds Ball x,r c= cl_Ball x,r
let x be Point of (TOP-REAL n); :: thesis: Ball x,r c= cl_Ball x,r
reconsider e = x as Point of (Euclid n) by TOPREAL3:13;
( Ball x,r = Ball e,r & cl_Ball x,r = cl_Ball e,r ) by Th13, Th14;
hence Ball x,r c= cl_Ball x,r by METRIC_1:15; :: thesis: verum