Theorems · Theorem · order theory
Finpartition.parts_eq_empty_iff
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a : α} {P : Finpartition a}, P.parts = ∅ ↔ a = ⊥- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Bot.botstatement and proof · cited by 4,720
- LE.le.transproof · cited by 3,151
- OrderBotstatement and proof · cited by 1,055
- Latticestatement and proof · cited by 916
- Eq.leproof · cited by 605
- Finset.supproof · cited by 530
- Finpartitionstatement and proof · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- le_bot_iffproof · cited by 116
- Finset.le_supproof · cited by 112
- Finset.sup_emptyproof · cited by 72
Cited by2
Results whose statement or proof uses this declaration.
- Finpartition.card_mod_card_parts_leproof · cited by 1
- Finpartition.parts_nonempty_iffproof · cited by 1