Theorems · Theorem · order theory
sup_top_eq
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderTop α] (a : α), a ⊔ ⊤ = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- SemilatticeSupOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- SemilatticeSupstatement and proof · cited by 785
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- sup_of_le_rightproof · cited by 143
Cited by6
Results whose statement or proof uses this declaration.
- Finset.inf_sup_distrib_leftproof · cited by 3
- isCompl_bot_topproof · cited by 2
- IsCompl.sup_infproof · cited by 2
- Set.union_univproof · cited by 1
- Ideal.sup_prod_eq_topproof · cited by 1
- max_top_rightproof · cited by 0