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 Th7:
  for f being convergent Real_Sequence holds
  lim (t + f) = t + lim f
  proof
    let f be convergent Real_Sequence;
    reconsider r = t as Element of REAL by XREAL_0:def 1;
    f + (NAT --> t) = t + f by Th5;
    hence lim (t + f) = lim (NAT --> r) + lim f by SEQ_2:6
    .= t + lim f by Th6;
  end;
