Theorems · Theorem · order theory
isMax_iff_eq_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, IsMax a ↔ a = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- IsMaxstatement and proof · cited by 372
- IsMax.eq_of_leproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- not_isMax_iff_ne_topproof · cited by 5
- IsMax.eq_topproof · cited by 3
- PrimitiveSpectrum.hull_finsetInfproof · cited by 2
- Order.succ_topproof · cited by 1
- Order.succ_le_iff_eq_topproof · cited by 0
- Order.isPredLimit_iff_of_orderTopproof · cited by 0