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

theorem
  for x being Real holds left_closed_halfline x is closed Subset
  of Sorgenfrey-line
proof
  let x be Real;
  set T = Sorgenfrey-line;
  reconsider A = right_open_halfline x as open Subset of T by TOPGEN_3:14;
  the carrier of T = REAL by TOPGEN_3:def 2;
  then (left_closed_halfline x)`` = A` by XXREAL_1:224,288;
  hence thesis;
end;
