Theorems · Theorem · order theory
top_inf_eq
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderTop α] (a : α), ⊤ ⊓ a = a- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- SemilatticeInfOrderTop
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
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- inf_of_le_rightproof · cited by 128
Cited by30
Results whose statement or proof uses this declaration.
- Set.univ_interproof · cited by 258
- himp_eq_top_iffproof · cited by 5
- Subfield.lift_relrank_comapproof · cited by 4
- sInf_le_sInf_of_subset_insert_topproof · cited by 4
- AddSubgroup.addSubgroupOf_eq_topproof · cited by 3
- Codisjoint.codisjoint_inf_right_of_codisjoint_inf_leftproof · cited by 2
- Ideal.comap_jacobson_of_surjectiveproof · cited by 2
- IsCompl.sup_infproof · cited by 2
- Codisjoint.le_of_disjointproof · cited by 2
- sup_himp_self_leftproof · cited by 2
- Finset.inf'_inductionproof · cited by 2
- Filter.top_prodproof · cited by 2