Theorems · Theorem · order theory
Finpartition.atomise_empty
∀ {α : Type u_1} [inst : DecidableEq α] {s : Finset α}, s.Nonempty → (Finpartition.atomise s ∅).parts = {s}- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.filterproof · cited by 949
- Finset.imageproof · cited by 910
- Finpartition.partsstatement and proof · cited by 184
- Finset.filter_congrproof · cited by 167
- Finset.powersetproof · cited by 93
- Finset.erase_eq_of_notMemproof · cited by 30
- Finset.Nonempty.ne_emptyproof · cited by 22
- Finset.image_singletonproof · cited by 21
- Finset.filter_trueproof · cited by 14
- Finset.notMem_singletonproof · cited by 13
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