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

theorem Th6:
  for m,n be Integer holds (exp_R(x)) #R (m/n) = exp_R(m/n*x)
proof
  let m,n be Integer;
  thus exp_R(m/n*x) = exp_R(x/n*m) by XCMPLX_1:75
    .=(exp_R(x/n)) #R m by Lm2
    .=((exp_R(x)) #R (1/n)) #R m by Th5
    .=(exp_R(x)) #R ((1/n)*m) by PREPOWER:91,SIN_COS:55
    .=(exp_R(x)) #R ((m/n)*1) by XCMPLX_1:75
    .=(exp_R(x)) #R (m/n);
end;
