Theorems · Theorem · order theory
sup_eq_bot_iff
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {a b : α}, a ⊔ b = ⊥ ↔ a = ⊥ ∧ b = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- SemilatticeSupOrderBot
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.
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- eq_bot_iffproof · cited by 159
- sup_le_iffproof · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- max_eq_botproof · cited by 3
- bihimp_eq_botproof · cited by 0
- Finset.union_eq_emptyproof · cited by 0