Theorems · Theorem · order theory
Finpartition.bot_notMem
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a : α} (self : Finpartition a), ⊥ ∉ self.partsNo element of the partition is bottom
- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · 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 · cited by 184
Cited by8
Results whose statement or proof uses this declaration.
- Finpartition.ne_botproof · cited by 7
- Finpartition.copyproof · cited by 3
- Finpartition.parts_eq_empty_iffproof · cited by 2
- MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiffproof · cited by 1
- MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiffUnionproof · cited by 1
- MeasureTheory.IsSetSemiring.empty_notMem_disjointOfUnionproof · cited by 1
- Finpartition.empty_notMem_partsproof · cited by 0
- Finpartition.isPartition_partsproof · cited by 0