Theorems · Theorem · order theory
Order.height_le_coe_iff
∀ {α : Type u_1} [inst : Preorder α] {x : α} {n : ℕ}, Order.height x ≤ ↑n ↔ ∀ y < x, Order.height y < ↑n- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- ENatstatement and proof · cited by 4,985
- Nat.cast_oneproof · cited by 2,501
- ENat.recTopCoeproof · cited by 75
- Order.heightstatement and proof · cited by 67
- top_addproof · cited by 55
- iSup₂_le_iffproof · cited by 19
- Order.height_eq_iSup_lt_heightproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Order.height_eq_zeroproof · cited by 4
- Ideal.height_le_iffproof · cited by 3
- Order.height_eq_coe_add_one_iffproof · cited by 2
- Order.height_natproof · cited by 1
- Order.coheight_le_coe_iffproof · cited by 0