reserve p, q, x, y for Real,
  n for Nat;

theorem
  for f being Element of REAL n, p being Point of I[01] holds |.p*f.| <= |.f.|
proof
  let f be Element of REAL n, p be Point of I[01];
  [. 0,1 .] = {r where r is Real: 0 <= r & r <= 1 } &
   p in the carrier of I[01] by RCOMP_1:def 1;
  then ex r being Real st r = p & 0 <= r & r <= 1 by BORSUK_1:40;
  hence thesis by Th10;
end;
