proposition: Lemma invert_nat_fun_sat2 f y (F : f 0 <= y < f (S y)) : f (invert_nat_fun f y) <= y < f (S (invert_nat_fun f y)).
proof: Proof. rewrite <- Nat.leb_le in *. rewrite <- Nat.ltb_lt in *; desc. rewrite Nat.ltb_antisym, Bool.negb_true_iff in *. apply find_max_sat2 with (f := fun x => f x <=? y); ins. Qed.
imports: NPeano Arith micromega.Lia Setoid HahnBase