Theorems · Theorem · order theory
Finpartition.card_filter_atomise_le_two_pow
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Finset α} {F : Finset (Finset α)},
t ∈ F → {u ∈ (Finpartition.atomise s F).parts | u ⊆ t ∧ u.Nonempty}.card ≤ 2 ^ (F.card - 1)- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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Cites20
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
- LE.le.transproof · cited by 3,151
- Finset.cardstatement and proof · cited by 2,327
- le_reflproof · cited by 2,061
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.filterstatement and proof · cited by 949
- Finset.imageproof · cited by 910
- Finset.eraseproof · cited by 455
- Finset.mem_filterproof · cited by 185
- Finpartition.partsstatement and proof · cited by 184
- Finset.filter_congrproof · cited by 167
- Finset.card_le_cardproof · cited by 118
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