reserve c for Complex;
reserve r for Real;
reserve m,n for Nat;
reserve f for complex-valued Function;
reserve f,g for differentiable Function of REAL,REAL;
reserve L for non empty ZeroStr;
reserve x for Element of L;
reserve p,q for Polynomial of F_Real;

theorem Th43:
  for r being Element of F_Real holds power(r,n) = ( #Z n).r
  proof
    let r be Element of F;
    thus power(r,n) = 1.F * power(r,n)
    .= FPower(1.F,n).r by POLYNOM5:def 12
    .= ( #Z n).r by Th40;
  end;
