Theorems · Theorem · order theory
IsCoatom.sup_eq_top_of_ne
∀ {α : Type u_2} [inst : SemilatticeSup α] [inst_1 : OrderTop α] {a b : α}, IsCoatom a → IsCoatom b → a ≠ b → a ⊔ b = ⊤- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSupOrderTop
Around this declaration
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Cites6
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
- IsCoatomstatement and proof · cited by 114
- codisjoint_iffproof · cited by 53
- IsCoatom.codisjoint_of_neproof · cited by 2
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