let n be Element of NAT ; :: thesis: for p being Point of (TOP-REAL n) holds dist p,p = 0
let p be Point of (TOP-REAL n); :: thesis: dist p,p = 0
ex a, b being Point of (Euclid n) st
( a = p & b = p & dist a,b = dist p,p ) by Def1;
hence dist p,p = 0 by METRIC_1:1; :: thesis: verum