proposition: Lemma size_4 u v w y z : exp_size (If w y z) < exp_size (If (If u v w) y z).
proof: Proof. simp exp_size. assert (1 + exp_size y + exp_size z > 0) by lia. revert H. generalize (1 + exp_size y + exp_size z). intros n Hn. generalize (exp_size_pos u). intros. rewrite 2 Nat.mul_add_distr_l. nia. Qed.
imports: Equations(Equations) List Program.Syntax Arith Lia