Theorems · Theorem · order theory
antitone_nat_of_succ_le
∀ {α : Type u} [inst : Preorder α] {f : ℕ → α}, (∀ (n : ℕ), f (n + 1) ≤ f n) → Antitone f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 25 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
- Antitonestatement · cited by 563
- monotone_nat_of_le_succproof · cited by 45
Cited by21
Results whose statement or proof uses this declaration.
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosedproof · cited by 4
- Subgroup.lowerCentralSeries_antitoneproof · cited by 3
- NNReal.agmSequences_monotone_and_antitoneproof · cited by 2
- AddSubgroup.lowerCentralSeries_antitoneproof · cited by 2
- pow_right_anti₀proof · cited by 2
- Ideal.Filtration.antitoneproof · cited by 2
- preCantorSet_antitoneproof · cited by 2
- PairReduction.antitone_logSizeBallSeq_add_one_subsetproof · cited by 2
- isAddFreimanHom_antitoneproof · cited by 1
- Finset.image_iterate_stabilises_lt_cardproof · cited by 1
- CantorScheme.ClosureAntitone.map_of_vanishingDiamproof · cited by 1