True ↔ ∃ d, StrictMono d ∧ 1 ≤ d 0 ∧ (Set.range d).HasDensity 1 ∧ Set.InjOn (fun x => match x with | (u, v) => ∏ i ∈ Finset.Icc u v, d i) {(u, v) | u ≤ v}