Theorems · Theorem · combinatorics
Fintype.card_piFinset
∀ {ι : Type u_4} {α : ι → Type u_6} [inst : DecidableEq ι] [inst_1 : Fintype ι] (s : (i : ι) → Finset (α i)),
(Fintype.piFinset s).card = ∏ i, (s i).card- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Finset.cardstatement and proof · cited by 2,327
- Finset.mem_univproof · cited by 361
- Finset.card_mapproof · cited by 114
- Fintype.piFinsetstatement · cited by 86
- Finset.card_piproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Fintype.card_piproof · cited by 12
- Pi.card_Iccproof · cited by 4
- Fintype.card_filter_piFinset_eq_of_memproof · cited by 2
- Fintype.card_piFinset_constproof · cited by 2
- Behrend.card_boxproof · cited by 1
- Pi.card_Iciproof · cited by 1
- Pi.card_Iicproof · cited by 1
- ZLattice.sum_piFinset_Icc_rpow_leproof · cited by 1
- MultilinearMap.map_sum_finset_auxproof · cited by 1
- ProbabilityTheory.uniformOn_piproof · cited by 0