reserve n for Nat,
  i for Integer,
  p, x, x0, y for Real,
  q for Rational,
  f for PartFunc of REAL,REAL;

theorem Th4:
  exp_R(-x) = 1/exp_R(x)
proof
  reconsider x as Real;
  exp_R(-x)*exp_R(x)=exp_R((-x)+x) by SIN_COS:50
    .=1 by SIN_COS:51;
  hence thesis by XCMPLX_1:73;
end;
