reserve E,F,G for RealNormSpace;
reserve f for Function of E,F;
reserve g for Function of F,G;
reserve a,b,c for Point of E;
reserve t for Real;

theorem Th10:
  for f being convergent Real_Sequence holds
  lim (f * a) = (lim f) * a
  proof
    let f be convergent Real_Sequence;
    f (#) (NAT --> a) = f * a by Th8;
    hence lim (f * a) = lim f * lim (NAT --> a) by NDIFF_1:14,18
    .= (lim f) * a by Th9;
  end;
