let n be Nat; :: thesis: for p being Point of (TOP-REAL n)
for r being Real holds the carrier of (Tball (p,r)) = Ball (p,r)
let p be Point of (TOP-REAL n); :: thesis: for r being Real holds the carrier of (Tball (p,r)) = Ball (p,r)
let r be Real; :: thesis: the carrier of (Tball (p,r)) = Ball (p,r)
[#] (Tball (p,r)) = Ball (p,r) by PRE_TOPC:def 5;
hence the carrier of (Tball (p,r)) = Ball (p,r) ; :: thesis: verum