reserve a,b,c,k,k9,m,n,n9,p,p9 for Nat;
reserve i,i9 for Integer;

theorem Th3:
  i is even implies i^2 mod 4 = 0
proof
  given i9 such that
A1: i = 2*i9;
  i^2 = 4*(i9^2) + 0 by A1;
  hence i^2 mod 4 = 0 mod 4 by NAT_D:61
    .= 0 by NAT_D:24;
end;
