reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

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;
