reserve x for set;
reserve a, b, c, d, e for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p for Rational;

theorem Th32:
  a>0 implies (1/a) to_power b = a to_power (-b)
proof
  assume
A1: a>0;
  hence (1/a) to_power b = (1/a) #R b by Def2
    .= 1/a #R b by A1,PREPOWER:79
    .= 1/a to_power b by A1,Def2
    .= a to_power (-b) by A1,Th28;
end;
