
theorem th0a:
for n,m being Nat holds n +` m = n + m & n *` m = n * m
proof
let n,m be Nat;
thus n +` m = card n +` card m
           .= card(n + m) by CARD_2:38
           .= n + m;
thus n *` m = card [:n,m:] by CARD_2:def 2
           .= card n * card m by CARD_2:46
           .= n * m;
end;
