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

theorem Th5:
  (exp_R(x)) #R (1/i) = exp_R(x/i)
proof
  set n = i;
  per cases;
  suppose
A1: n <> 0;
    then exp_R(x) =exp_R((x/n)*n) by XCMPLX_1:87
      .=(exp_R(x/n)) #R n by Lm2;
    hence (exp_R(x)) #R (1/n) =(exp_R(x/n)) #R (n* (1/n) ) by PREPOWER:91
,SIN_COS:55
      .=(exp_R(x/n)) #R 1 by A1,XCMPLX_1:106
      .=exp_R(x/n) by PREPOWER:72,SIN_COS:55;
  end;
  suppose
A2: n = 0;
    (exp_R(x)) #R (1/0) = exp_R(0) by PREPOWER:71,SIN_COS:51,55
      .= exp_R(x/0) by XCMPLX_1:49;
    hence thesis by A2;
  end;
end;
