Theorems · Theorem · order theory
Fin.monotone_iff_le_succ
∀ {n : ℕ} {α : Type u_1} [inst : Preorder α] {f : Fin (n + 1) → α}, Monotone f ↔ ∀ (i : Fin n), f i.castSucc ≤ f i.succA function f on Fin (n + 1) is monotone if and only if f i ≤ f (i + 1) for all i.
- Defined in
- Mathlib.Order.Fin.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 30 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.
Cites4
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
- monotone_iff_forall_ltproof · cited by 9
- Fin.liftFun_iff_succproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Module.Basis.flag_monoproof · cited by 1
- Fin.insertNth_last_monotoneproof · cited by 0
- Fin.insertNth_zero_monotoneproof · cited by 0
- Fin.insertNth_monotoneproof · cited by 0
- IsMaxChain.range_fin_of_covByproof · cited by 0