Theorems · Theorem · order theory
Fin.insertNth_last_monotone
∀ {n : ℕ} {α : Type u_1} [inst : Preorder α] {f : Fin (n + 1) → α},
Monotone f → ∀ (x : α), f (Fin.last n) ≤ x → Monotone ((Fin.last (n + 1)).insertNth x f)- Defined in
- Mathlib.Order.Fin.InsertNth
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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- Preorderstatement and proof · cited by 7,952
- Monotonestatement and proof · cited by 1,397
- Fin.insertNthstatement · cited by 95
- Fin.snoc_castSuccproof · cited by 38
- Fin.insertNth_apply_sameproof · cited by 30
- Fin.castSucc_le_succproof · cited by 17
- Fin.eq_castSucc_or_eq_lastproof · cited by 13
- Fin.insertNth_last'proof · cited by 6
- Fin.monotone_iff_le_succproof · cited by 5
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