Theorems · Theorem · order theory
Fin.insertNth_zero_monotone
∀ {n : ℕ} {α : Type u_1} [inst : Preorder α] {f : Fin (n + 1) → α},
Monotone f → ∀ x ≤ f 0, Monotone (Fin.insertNth 0 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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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
- Fin.insertNthstatement · cited by 95
- Fin.cons_succproof · cited by 54
- Fin.insertNth_apply_sameproof · cited by 30
- Fin.castSucc_le_succproof · cited by 17
- Fin.cons_oneproof · cited by 10
- Fin.monotone_iff_le_succproof · cited by 5
- Fin.insertNth_zero'proof · cited by 5
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