def g (x : Nat) : List (Nat × List Nat) :=
[(x, [x, x]), (x, [])]

def h (x : Nat) : List (Nat × List Nat) :=
g x |>.filter fun ⟨_, xs⟩ => xs.isEmpty

theorem ex1 : g 10 = [(10, [10, 10]), (10, [])] :=
rfl

theorem ex2 : h 10 = [(10, [])] :=
rfl