Theorems · Theorem · order theory
Fin.insertNth_monotone
∀ {n : ℕ} {α : Type u_1} [inst : Preorder α] {f : Fin (n + 1) → α},
Monotone f → ∀ (i : Fin n) (x : α), f i.castSucc ≤ x → x ≤ f i.succ → Monotone (i.castSucc.succ.insertNth x f)- Defined in
- Mathlib.Order.Fin.InsertNth
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
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Cites11
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 and proof · cited by 1,397
- lt_trichotomyproof · cited by 178
- Fin.insertNthstatement and proof · cited by 95
- Fin.ne_zero_of_ltproof · cited by 32
- Fin.insertNth_apply_sameproof · cited by 30
- Fin.ne_last_of_ltproof · cited by 25
- Fin.insertNth_apply_succAboveproof · cited by 23
- Fin.eq_castSucc_of_ne_lastproof · cited by 9
- Fin.monotone_iff_le_succproof · cited by 5
- Fin.succAbove_succ_selfproof · cited by 4
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