Theorems · Theorem · order theory
Finpartition.ne_bot
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a : α} (P : Finpartition a) {b : α}, b ∈ P.parts → b ≠ ⊥- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Latticestatement and proof · cited by 916
- Finpartitionstatement and proof · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- Finpartition.bot_notMemproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Finpartition.nonempty_of_mem_partsproof · cited by 4
- Finpartition.exists_le_of_leproof · cited by 1
- Finpartition.sum_combineproof · cited by 1
- Finpartition.card_monoproof · cited by 1
- MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnionproof · cited by 1
- Finpartition.card_bindproof · cited by 1
- Finpartition.ne_emptyproof · cited by 1