theorem Th26:
  for S being Subset of R^1 st S = RAT holds
  RAT /\ ]. -infty,r .[ is open Subset of R^1 | S
  proof
    let S be Subset of R^1 such that
A1: S = RAT;
    set X = ]. -infty,r .[;
    reconsider R = RAT /\ X as Subset of RR by Lm8,XBOOLE_1:17;
A2: R^1(X) is open by BORSUK_5:40;
    R = R^1(X) /\ the carrier of RR by PRE_TOPC:8;
    hence thesis by A1,A2,TSP_1:def 1;
  end;
