Theorems · Theorem · order theory
Order.height_coe_withBot
∀ {α : Type u_1} [inst : Preorder α] (x : α), Order.height ↑x = Order.height x + 1- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 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.
Cites34
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.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- Bot.botproof · cited by 4,720
- Nat.cast_oneproof · cited by 2,501
- le_antisymmproof · cited by 2,068
- Nat.cast_zeroproof · cited by 1,870
- WithBotstatement and proof · cited by 1,498
- Nat.cast_addproof · cited by 586
- SetRelproof · cited by 581
- WithBot.somestatement and proof · cited by 541
- RelSeries.lengthproof · cited by 195
Cited by1
Results whose statement or proof uses this declaration.
- Order.coheight_coe_withTopproof · cited by 1