Theorems · Theorem · order theory
Order.one_lt_height_iff
∀ {α : Type u_1} [inst : Preorder α] {x : α}, 1 < Order.height x ↔ ∃ y, ∃ z < y, y < x- Defined in
- Mathlib.Order.KrullDimension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Order.heightstatement and proof · cited by 67
- one_add_one_eq_twoproof · cited by 65
- RelSeries.toListproof · cited by 25
- ENat.one_ne_topproof · cited by 15
- ENat.add_one_le_iffproof · cited by 11
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