reserve a,b,c,k,m,n for Nat;
reserve p for Prime;

theorem Th21:
  n divides 4 implies n = 1 or n = 2 or n = 4
  proof
    assume
A1: n divides 4;
    then n <= 4 by INT_2:27;
    then
A2: n = 0 or ... or n = 4;
    now
      (3*1+1) mod 3 = 1 mod 3 by NAT_D:21
      .= 1 by NAT_D:24;
      hence not 3 divides 4 by INT_1:62;
    end;
    hence thesis by A1,A2;
  end;
