
theorem Th32:
  for r being Real holds r in the carrier of I(01) iff 0 < r & r < 1
proof
  let r be Real;
  hereby
    assume r in the carrier of I(01);
    then r in ]. 0, 1 .[ by Def1;
    hence 0 < r & r < 1 by XXREAL_1:4;
  end;
  assume that
A1: 0 < r and
A2: r < 1;
  r in ]. 0, 1 .[ by A1,A2,XXREAL_1:4;
  hence thesis by Def1;
end;
