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

theorem Th9:
  (exp_R(1)) #R x =exp_R(x) & (exp_R(1)) to_power x = exp_R(x) &
  number_e to_power x = exp_R(x) & number_e #R x = exp_R(x)
proof
  thus
A1: exp_R(x) =exp_R(x*1) .= (exp_R(1)) #R x by Th8;
  exp_R(1) > 0 by SIN_COS:55;
  hence thesis by A1,IRRAT_1:def 7,POWER:def 2;
end;
