
theorem Lemma3ArProg:
  for i being Nat holds not 3 divides ArProg (2,3).i
  proof
    let i be Nat;
    assume 3 divides ArProg (2,3).i; then
A1: 3 divides 2 + 3 * i by ArDefNth;
    3 divides 3 * i; then
    3 divides 2 + 3 * i - 3 * i by A1,PREPOWER:94;
    hence thesis by INT_2:28;
  end;
