Theorems · Definition · order theory
WCovBy
{α : Type u_1} → [Preorder α] → α → α → PropWCovBy a b means that a = b or b covers a.
This means that a ≤ b and there is no element in between. This is denoted a ⩿ b.
- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 107 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by109
Results whose statement or proof uses this declaration.
- WCovBy.lestatement and proof · cited by 15
- CovBy.wcovBystatement · cited by 15
- WCovBy.covBy_of_ltstatement and proof · cited by 6
- WCovBy.eq_or_eqstatement and proof · cited by 5
- Set.OrdConnected.apply_wcovBy_apply_iffstatement and proof · cited by 5
- Set.wcovBy_insertstatement · cited by 4
- WCovBy.le_succstatement · cited by 3
- wcovBy_eq_reflGen_covBystatement · cited by 3
- wcovBy_iff_covBy_or_le_and_lestatement and proof · cited by 3
- Order.pred_wcovBystatement · cited by 3
- Order.wcovBy_succstatement · cited by 3
- Pi.exists_forall_antisymmRel_of_wcovBystatement and proof · cited by 3