let n be Element of NAT ; :: thesis: for r being real number
for y being Point of (TOP-REAL n) st y in cl_Ball (0. (TOP-REAL n)),r holds
|.y.| <= r
let r be real number ; :: thesis: for y being Point of (TOP-REAL n) st y in cl_Ball (0. (TOP-REAL n)),r holds
|.y.| <= r
let y be Point of (TOP-REAL n); :: thesis: ( y in cl_Ball (0. (TOP-REAL n)),r implies |.y.| <= r )
assume y in cl_Ball (0. (TOP-REAL n)),r ; :: thesis: |.y.| <= r
then |.(y - (0. (TOP-REAL n))).| <= r by Th8;
hence |.y.| <= r by RLVECT_1:26; :: thesis: verum