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

theorem Th62:
  for x being Real st x < 0 holds absreal.x = -x
proof
  let x be Real;
  assume
A1: 0 > x;
  absreal.x = |.x.| by EUCLID:def 2
    .= -x by A1,ABSVALUE:def 1;
  hence thesis;
end;
