reserve x, r for Real;
reserve A for symmetrical Subset of COMPLEX;
reserve F,G for PartFunc of REAL, REAL;

theorem
  for A being symmetrical Subset of REAL holds |. cos .| is_even_on A
proof
  let A be symmetrical Subset of REAL;
  A is symmetrical Subset of COMPLEX by NUMBERS:11,XBOOLE_1:1;
  hence thesis by Th21,Th66;
end;
