
theorem for a,b,c be Nat holds
  (a mod c)*(b mod c) = c implies a*b mod c = 0
  proof
    let a,b,c be Nat;
    assume (a mod c)*(b mod c) = c; then
    c mod c = ((a mod c)*(b mod c)) mod c;
    hence thesis by NAT_D:67;
  end;
