Theorems · Theorem · order theory
inf_eq_top_iff
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {a b : α}, a ⊓ b = ⊤ ↔ a = ⊤ ∧ b = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- SemilatticeInfOrderTop
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
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- eq_top_iffproof · cited by 236
- top_le_iffproof · cited by 175
- le_inf_iffproof · cited by 48
Cited by7
Results whose statement or proof uses this declaration.
- Finset.inf_eq_top_iffproof · cited by 3
- List.minimum_ne_top_of_length_posproof · cited by 2
- symmDiff_eq_topproof · cited by 0
- bihimp_eq_topproof · cited by 0
- min_eq_topproof · cited by 0
- List.minimum_ne_top_of_ne_nilproof · cited by 0
- Finset.inter_eq_univproof · cited by 0