Theorems · Theorem · order theory
Order.exists_series_of_le_coheight
∀ {α : Type u_1} [inst : Preorder α] (a : α) {n : ℕ}, ↑n ≤ Order.coheight a → ∃ p, RelSeries.head p = a ∧ p.length = n- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
Cites12
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
- Set.ofPredstatement · cited by 6,101
- ENatstatement · cited by 4,985
- OrderDualproof · cited by 927
- RelSeries.lengthstatement and proof · cited by 195
- RelSeries.lastproof · cited by 114
- RelSeries.headstatement · cited by 89
- LTSeriesstatement and proof · cited by 87
- Order.coheightstatement and proof · cited by 74
- RelSeries.reverseproof · cited by 11
- RelSeries.reverse_lengthproof · cited by 4
- Order.exists_series_of_le_heightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Order.exists_series_of_coheight_eq_coeproof · cited by 1