
theorem Lm2:
for p being Prime
for R being p-characteristic commutative Ring
for a being Element of R, n being Nat st p divides n holds n * a = 0.R
proof
let p be Prime, R be p-characteristic commutative Ring;
let a be Element of R, n be Nat;
assume p divides n; then
ex x being Nat st p * x = n by NAT_D:def 3;
hence thesis by Lm1;
end;
