
theorem SM3:
  for s be square Integer holds s mod 3 is trivial Nat
  proof
    let s be square Integer;
    2-root s is integer; then
    reconsider a = 2-root s as integer number;
    a|^2,0 are_congruent_mod 3 or a|^2,1 are_congruent_mod 3 by NAT_6:15; then
    a|^2 mod 3 = 0 mod 3 or a|^2 mod 3 = 1 mod (1 + 2) by NAT_D:64;
    hence thesis by NAT_2:def 1;
  end;
