Theorems · Inductive type · order theory
OrderBot
(α : Type u) → [LE α] → Type u
An order is an OrderBot if it has a least element.
We state this using a data mixin, holding the value of ⊥ and the least element constraint.
- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 1,055 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by1,363
Results whose statement or proof uses this declaration.
- Disjointstatement and proof · cited by 2,201
- Finset.supstatement and proof · cited by 530
- bot_lestatement and proof · cited by 306
- Set.PairwiseDisjointstatement and proof · cited by 275
- Finpartitionstatement · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- eq_bot_iffstatement and proof · cited by 159
- IsAtomstatement and proof · cited by 130
- Disjoint.symmstatement and proof · cited by 125
- le_bot_iffstatement and proof · cited by 116
- Ne.bot_ltstatement and proof · cited by 116
- Finset.le_supstatement and proof · cited by 112
Showing the 200 most cited of 1,363.