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 Th5:
  for f being Real_Sequence holds f + (NAT --> t) = t + f
  proof
    let f be Real_Sequence;
    let n be Element of NAT;
    thus (f + (NAT --> t)).n = f.n + (NAT --> t).n by VALUED_1:1
    .= (f + t).n by VALUED_1:2;
  end;
