let n be Element of NAT ; :: thesis: for r being real number
for x being Point of (TOP-REAL n) holds Sphere x,r c= cl_Ball x,r
let r be real number ; :: thesis: for x being Point of (TOP-REAL n) holds Sphere x,r c= cl_Ball x,r
let x be Point of (TOP-REAL n); :: thesis: Sphere x,r c= cl_Ball x,r
reconsider e = x as Point of (Euclid n) by TOPREAL3:13;
( Sphere x,r = Sphere e,r & cl_Ball x,r = cl_Ball e,r ) by Th14, Th15;
hence Sphere x,r c= cl_Ball x,r by METRIC_1:16; :: thesis: verum