let n be Nat; :: thesis: for p being Point of (TOP-REAL n) holds
( p <> 0. (TOP-REAL n) iff |.p.| > 0 )
let p be Point of (TOP-REAL n); :: thesis: ( p <> 0. (TOP-REAL n) iff |.p.| > 0 )
( p <> 0. (TOP-REAL n) implies |.p.| > 0 )

proof

assume A1: p <> 0. (TOP-REAL n) ; :: thesis: |.p.| > 0
( n in NAT & 0 <= |.p.| ) by Th36, ORDINAL1:def 12;
hence |.p.| > 0 by A1, TOPRNS_1:24, XXREAL_0:1; :: thesis: verum

end;

hence ( p <> 0. (TOP-REAL n) iff |.p.| > 0 ) by Th37; :: thesis: verum