
theorem
  for a be Nat, b,c be non zero Nat holds
  (a mod c) * (b mod c) >= (a*b) mod c
  proof
    let a be Nat ,b,c be non zero Nat;
    ((a mod c)*(b mod c)) mod c <= (a mod c)*(b mod c) by AMB;
    hence thesis by NAT_D:67;
  end;
