reserve r, s, t for Real;
reserve seq for Real_Sequence,
  X, Y for Subset of REAL;
reserve r3, r1, q3, p3 for Real;

theorem
  for A being Subset of REAL, x being Real st x in --A holds
    ex a being Real st a in A & x = -a
proof
  let A be Subset of REAL,
      x be Real;
  assume x in --A; then
  x in {-a where a is Complex: a in A}; then
  consider a being Complex such that
A1: x = -a & a in A;
  reconsider a as Real by A1;
  take a;
  thus thesis by A1;
end;
