Theorems · Theorem · order theory
Partition.mem_top_iff
∀ {α : Type u_1} {s : α} [inst : CompleteLattice α] {a : α}, a ∈ ⊤ ↔ a = s ∧ a ≠ ⊥- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- CompleteLatticestatement and proof · cited by 1,048
- Set.mem_singleton_iffproof · cited by 172
- Partitionstatement and proof · cited by 91
- sSup_singletonproof · cited by 14
- sSupIndep_singletonproof · cited by 3
- Partition.top_defproof · cited by 1
- Partition.mem_removeBotproof · cited by 1
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