Theorems · Theorem · order theory
Order.coe_lt_height_iff
∀ {α : Type u_1} [inst : Preorder α] {x : α} {n : ℕ},
Order.height x < ⊤ → (↑n < Order.height x ↔ ∃ y < x, Order.height y = ↑n)- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- ENatstatement and proof · cited by 4,985
- LT.lt.leproof · cited by 2,189
- lt_of_le_of_ltproof · cited by 432
- RelSeries.lengthproof · cited by 195
- RelSeries.lastproof · cited by 114
- RelSeries.toFunproof · cited by 114
- LTSeriesproof · cited by 87
- Order.heightstatement and proof · cited by 67
- LT.lt.ne_topproof · cited by 34
- LTSeries.strictMonoproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Order.height_eq_coe_add_one_iffproof · cited by 2
- Order.coe_lt_coheight_iffproof · cited by 0