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

theorem Th57:
  for x being Real st x < 0 holds signum.x = -1
proof
  let x be Real;
  assume
A1: 0 > x;
  signum.x = sgn x by Def9
    .= -1 by A1,ABSVALUE:def 2;
  hence thesis;
end;
