Theorems · Theorem · order theory
top_sup_eq
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderTop α] (a : α), ⊤ ⊔ a = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 8 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_leftproof · cited by 218
Cited by8
Results whose statement or proof uses this declaration.
- isCompl_top_botproof · cited by 5
- Set.univ_unionproof · cited by 2
- Ideal.natCast_eq_topproof · cited by 1
- Subgroup.map_eq_range_iffproof · cited by 1
- AddSubgroup.map_eq_range_iffproof · cited by 1
- max_top_leftproof · cited by 0
- map_commutator_eqproof · cited by 0
- map_addCommutator_eqproof · cited by 0