reserve a, b, r, s for Real;

theorem
  for X being Subset of R^1 st X = ].a,b.[ holds Int X = ].a,b.[
proof
  let X be Subset of R^1;
  assume
A1: X = ].a,b.[;
  then reconsider X as open Subset of R^1 by BORSUK_5:39;
  Int X = X by TOPS_1:23;
  hence thesis by A1;
end;
