
theorem Th10:
  for R being unital associative non empty multMagma,
  a being Element of R, n,m being Nat holds
  a|^(n+m) = (a|^n) * (a|^m)
proof
  let R be unital associative non empty multMagma, a be Element of R,
  n,m be Nat;
  reconsider n1 = n, m1 = m as Element of NAT by ORDINAL1:def 12;
  a|^(n1+m1) = (a|^n1) * (a|^m1) by Lm3;
  hence thesis;
end;
