
theorem LemmaBono:
  for i being Nat holds
    not 3 divides ArProg (2,3).i - 1
  proof
    let i be Nat;
    assume 3 divides ArProg (2,3).i - 1; then
    3 divides ((2 + 3 * i) - 1) by ArDefNth; then
    3 divides (1 + 3 * i) & 3 divides (3 * i); then
    3 divides (1 + 3 * i - 3 * i) by PREPOWER:94;
    hence thesis by NAT_D:7;
  end;
