
theorem
  for n be non zero Element of NAT,
      x be Element of REAL n, r be Real, i be Element of NAT holds
    proj(i,n).(r*x) = r*(proj(i,n).x)
proof
  let n be non zero Element of NAT,
    x be Element of REAL n, r be Real, i be Element of NAT;
 thus proj(i,n).(r*x) = (r*x).i by PDIFF_1:def 1
               .= r*(x.i) by RVSUM_1:44
               .= r*(proj(i,n).x) by PDIFF_1:def 1;
end;
