Theorems · Theorem · order theory
Partition.parts_nonempty
∀ {α : Type u_1} {s : α} [inst : CompleteLattice α] (P : Partition s), s ≠ ⊥ → (↑P).Nonempty- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Bot.botstatement and proof · cited by 4,720
- Set.Nonemptystatement · cited by 2,627
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Partitionstatement and proof · cited by 91
- sSup_emptyproof · cited by 19
- Partition.sSup_eqproof · cited by 4
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