
theorem Th23:
  for L being Field, x being Element of L st x <> 0.L for i,j,k
  being Nat holds pow(x,(i-1)*(k-1)) * pow(x,-(j-1)*(k-1)) = pow(x,(i-j)*(k-1))
proof
  let L be Field;
  let x be Element of L;
  assume
A1: x <> 0.L;
  let i,j,k be Nat;
  pow(x, (i-1)*(k-1)) * pow(x, -(j-1)*(k-1)) = pow(x, (i-1)*(k-1) + (-(j-1
  )*(k-1))) by A1,Th21
    .= pow(x, (i-j)*(k-1));
  hence thesis;
end;
