
theorem Fin1:
for R being finite Ring, n being Nat
holds card(the carrier of R^*n) = card(the carrier of R) |^ n
proof
let R be finite Ring, n be Nat;
set D = the carrier of R;
A: card(Seg n) = card n by FINSEQ_1:57;
B: card D = card D & n-tuples_on D = Funcs(Seg n,D) by FINSEQ_2:93;
thus card(the carrier of R^*n)
   = card Funcs(Seg n,D) by B,DEF
  .= card(the carrier of R) |^ n by A,CARD_FIN:4;
end;
