Theorems · Theorem · order theory
monotone_nat_of_le_succ
∀ {α : Type u} [inst : Preorder α] {f : ℕ → α}, (∀ (n : ℕ), f n ≤ f (n + 1)) → Monotone f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- Nat.rel_of_forall_rel_succ_of_leproof · cited by 1
Cited by45
Results whose statement or proof uses this declaration.
- Nat.mono_castproof · cited by 76
- antitone_nat_of_succ_leproof · cited by 21
- pow_right_mono₀proof · cited by 19
- eVariationOn.edist_leproof · cited by 7
- MeasureTheory.upperCrossingTime_monoproof · cited by 5
- Subgroup.upperCentralSeries_monoproof · cited by 5
- Nat.count_monotoneproof · cited by 4
- Filter.exists_seq_monotone_tendsto_atTop_atTopproof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Ici_zero_of_filterproof · cited by 3
- Monotone.monotone_iterate_of_le_mapproof · cited by 3
- List.monotone_sum_takeproof · cited by 3
- MeasureTheory.lowerCrossingTime_monoproof · cited by 3