reserve x,y for Real,
  u,v,w for set,
  r for positive Real;

theorem Th54:
  for x being Real holds left_open_halfline x is closed
  Subset of Sorgenfrey-line
proof
  let x be Real;
  set T = Sorgenfrey-line;
  reconsider A = right_closed_halfline x as open Subset of T by TOPGEN_3:15;
  the carrier of T = REAL by TOPGEN_3:def 2;
  then left_open_halfline x = A` by XXREAL_1:224,294;
  hence thesis;
end;
